--- _id: '14797' abstract: - lang: eng text: We study a random matching problem on closed compact 2 -dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers n and m=m(n) of points, asymptotically equivalent as n goes to infinity, the optimal transport plan between the two empirical measures μn and νm is quantitatively well-approximated by (Id,exp(∇hn))#μn where hn solves a linear elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère equation. This is obtained in the case of samples of correlated random points for which a stretched exponential decay of the α -mixing coefficient holds and for a class of discrete-time Markov chains having a unique absolutely continuous invariant measure with respect to the volume measure. acknowledgement: "NC has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No 948819).\r\nFM is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems. FM has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute for Mathematics in the Sciences." article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Nicolas full_name: Clozeau, Nicolas id: fea1b376-906f-11eb-847d-b2c0cf46455b last_name: Clozeau - first_name: Francesco full_name: Mattesini, Francesco last_name: Mattesini citation: ama: Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. 2024. doi:10.1007/s00440-023-01254-0 apa: Clozeau, N., & Mattesini, F. (2024). Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01254-0 chicago: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01254-0. ieee: N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic 2D-discrete random matching problem,” Probability Theory and Related Fields. Springer Nature, 2024. ista: Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. mla: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory and Related Fields, Springer Nature, 2024, doi:10.1007/s00440-023-01254-0. short: N. Clozeau, F. Mattesini, Probability Theory and Related Fields (2024). date_created: 2024-01-14T23:00:57Z date_published: 2024-01-04T00:00:00Z date_updated: 2024-01-17T11:18:34Z day: '04' ddc: - '510' department: - _id: JuFi doi: 10.1007/s00440-023-01254-0 ec_funded: 1 external_id: arxiv: - '2303.00353' has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00440-023-01254-0 month: '01' oa: 1 oa_version: Published Version project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: Probability Theory and Related Fields publication_identifier: eissn: - 1432-2064 issn: - 0178-8051 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Annealed quantitative estimates for the quadratic 2D-discrete random matching problem tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- _id: '14884' abstract: - lang: eng text: We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic energy functional with homogeneous coefficients. We provide explicit formulas for the effective magnetic properties of the composite material in terms of homogenization correctors. Additionally, the variational analysis of the two exchange energy terms is performed in the more general setting of functionals defined on manifold-valued maps with Sobolev regularity, in the case in which the target manifold is a bounded, orientable smooth surface with tubular neighborhood of uniform thickness. Eventually, we present an explicit characterization of minimizers of the effective exchange in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s predictions on the emergence of helical structures in composite ferromagnetic materials with stochastic microstructure. acknowledgement: All authors acknowledge support of the Austrian Science Fund (FWF) through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally been supported by the FWF through grants V662, Y1292, and P35359, as well as from OeAD through the WTZ grant CZ09/2023. article_number: '30' article_processing_charge: No article_type: original author: - first_name: Elisa full_name: Davoli, Elisa last_name: Davoli - first_name: Lorenza full_name: D’Elia, Lorenza last_name: D’Elia - first_name: Jonas full_name: Ingmanns, Jonas id: 71523d30-15b2-11ec-abd3-f80aa909d6b0 last_name: Ingmanns citation: ama: Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 2024;34(2). doi:10.1007/s00332-023-10005-3 apa: Davoli, E., D’Elia, L., & Ingmanns, J. (2024). Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-10005-3 chicago: Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science. Springer Nature, 2024. https://doi.org/10.1007/s00332-023-10005-3. ieee: E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions,” Journal of Nonlinear Science, vol. 34, no. 2. Springer Nature, 2024. ista: Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2), 30. mla: Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science, vol. 34, no. 2, 30, Springer Nature, 2024, doi:10.1007/s00332-023-10005-3. short: E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024). date_created: 2024-01-28T23:01:42Z date_published: 2024-01-23T00:00:00Z date_updated: 2024-02-05T08:54:44Z day: '23' department: - _id: JuFi doi: 10.1007/s00332-023-10005-3 external_id: arxiv: - '2306.05151' intvolume: ' 34' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2306.05151 month: '01' oa: 1 oa_version: Preprint project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Journal of Nonlinear Science publication_identifier: eissn: - 1432-1467 issn: - 0938-8974 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 34 year: '2024' ... --- _id: '12485' abstract: - lang: eng text: In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative noise are weakened considerably. Our new setting provides general conditions under which local and global existence and uniqueness hold. Moreover, we prove continuous dependence on the initial data. We show that many classical SPDEs, which could not be covered by the classical variational setting, do fit in the critical variational setting. In particular, this is the case for the Cahn-Hilliard equations, tamed Navier-Stokes equations, and Allen-Cahn equation. acknowledgement: The first author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819) . The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO). article_processing_charge: No article_type: original author: - first_name: Antonio full_name: Agresti, Antonio id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72 last_name: Agresti orcid: 0000-0002-9573-2962 - first_name: Mark full_name: Veraar, Mark last_name: Veraar citation: ama: Agresti A, Veraar M. The critical variational setting for stochastic evolution equations. Probability Theory and Related Fields. 2024. doi:10.1007/s00440-023-01249-x apa: Agresti, A., & Veraar, M. (2024). The critical variational setting for stochastic evolution equations. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01249-x chicago: Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic Evolution Equations.” Probability Theory and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01249-x. ieee: A. Agresti and M. Veraar, “The critical variational setting for stochastic evolution equations,” Probability Theory and Related Fields. Springer Nature, 2024. ista: Agresti A, Veraar M. 2024. The critical variational setting for stochastic evolution equations. Probability Theory and Related Fields. mla: Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic Evolution Equations.” Probability Theory and Related Fields, Springer Nature, 2024, doi:10.1007/s00440-023-01249-x. short: A. Agresti, M. Veraar, Probability Theory and Related Fields (2024). date_created: 2023-02-02T10:45:15Z date_published: 2024-02-02T00:00:00Z date_updated: 2024-02-26T09:39:07Z day: '02' department: - _id: JuFi doi: 10.1007/s00440-023-01249-x ec_funded: 1 external_id: arxiv: - '2206.00230' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00440-023-01249-x month: '02' oa: 1 oa_version: Preprint project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: Probability Theory and Related Fields publication_identifier: eissn: - 1432-2064 issn: - 0178-8051 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The critical variational setting for stochastic evolution equations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- _id: '15098' abstract: - lang: eng text: The paper is devoted to the analysis of the global well-posedness and the interior regularity of the 2D Navier–Stokes equations with inhomogeneous stochastic boundary conditions. The noise, white in time and coloured in space, can be interpreted as the physical law describing the driving mechanism on the atmosphere–ocean interface, i.e. as a balance of the shear stress of the ocean and the horizontal wind force. acknowledgement: The authors thank Professor Franco Flandoli for useful discussions and valuable insight into the subject. In particular, A.A. would like to thank professor Franco Flandoli for hosting and financially contributing to his research visit at Scuola Normale di Pisa in January 2023, where this work started. E.L. would like to express sincere gratitude to Professor Marco Fuhrman for igniting his interest in this particular field of research. E.L. want to thank Professor Matthias Hieber and Dr. Martin Saal for useful discussions. Finally, the authors thank the anonymous referee for helpful comments which improved the paper from its initial version.Open access funding provided by Scuola Normale Superiore within the CRUI-CARE Agreement. A. Agresti has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 948819). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Antonio full_name: Agresti, Antonio id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72 last_name: Agresti orcid: 0000-0002-9573-2962 - first_name: Eliseo full_name: Luongo, Eliseo last_name: Luongo citation: ama: Agresti A, Luongo E. Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. Mathematische Annalen. 2024. doi:10.1007/s00208-024-02812-0 apa: Agresti, A., & Luongo, E. (2024). Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-024-02812-0 chicago: Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.” Mathematische Annalen. Springer Nature, 2024. https://doi.org/10.1007/s00208-024-02812-0. ieee: A. Agresti and E. Luongo, “Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions,” Mathematische Annalen. Springer Nature, 2024. ista: Agresti A, Luongo E. 2024. Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. Mathematische Annalen. mla: Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.” Mathematische Annalen, Springer Nature, 2024, doi:10.1007/s00208-024-02812-0. short: A. Agresti, E. Luongo, Mathematische Annalen (2024). date_created: 2024-03-10T23:00:54Z date_published: 2024-02-27T00:00:00Z date_updated: 2024-03-13T12:20:23Z day: '27' department: - _id: JuFi doi: 10.1007/s00208-024-02812-0 ec_funded: 1 external_id: arxiv: - '2306.11081' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00208-024-02812-0 month: '02' oa: 1 oa_version: Published Version project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: Mathematische Annalen publication_identifier: eissn: - 1432-1807 issn: - 0025-5831 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- _id: '15119' abstract: - lang: eng text: In this paper we consider an SPDE where the leading term is a second order operator with periodic boundary conditions, coefficients which are measurable in (t,ω) , and Hölder continuous in space. Assuming stochastic parabolicity conditions, we prove Lp((0,T)×Ω,tκdt;Hσ,q(Td)) -estimates. The main novelty is that we do not require p=q . Moreover, we allow arbitrary σ∈R and weights in time. Such mixed regularity estimates play a crucial role in applications to nonlinear SPDEs which is clear from our previous work. To prove our main results we develop a general perturbation theory for SPDEs. Moreover, we prove a new result on pointwise multiplication in spaces with fractional smoothness. acknowledgement: The first author has been partially supported by the Nachwuchsring – Network for the promotion of young scientists – at TU Kaiserslautern. The second author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO). The authors thank the anonymous referees and Max Sauerbrey for careful reading and helpful suggestions. article_processing_charge: No article_type: original author: - first_name: Antonio full_name: Agresti, Antonio id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72 last_name: Agresti orcid: 0000-0002-9573-2962 - first_name: Mark full_name: Veraar, Mark last_name: Veraar citation: ama: Agresti A, Veraar M. Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions. Annales de l’institut Henri Poincare Probability and Statistics. 2024;60(1):413-430. doi:10.1214/22-AIHP1333 apa: Agresti, A., & Veraar, M. (2024). Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions. Annales de l’institut Henri Poincare Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/22-AIHP1333 chicago: Agresti, Antonio, and Mark Veraar. “Stochastic Maximal Lp(Lq)-Regularity for Second Order Systems with Periodic Boundary Conditions.” Annales de l’institut Henri Poincare Probability and Statistics. Institute of Mathematical Statistics, 2024. https://doi.org/10.1214/22-AIHP1333. ieee: A. Agresti and M. Veraar, “Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions,” Annales de l’institut Henri Poincare Probability and Statistics, vol. 60, no. 1. Institute of Mathematical Statistics, pp. 413–430, 2024. ista: Agresti A, Veraar M. 2024. Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions. Annales de l’institut Henri Poincare Probability and Statistics. 60(1), 413–430. mla: Agresti, Antonio, and Mark Veraar. “Stochastic Maximal Lp(Lq)-Regularity for Second Order Systems with Periodic Boundary Conditions.” Annales de l’institut Henri Poincare Probability and Statistics, vol. 60, no. 1, Institute of Mathematical Statistics, 2024, pp. 413–30, doi:10.1214/22-AIHP1333. short: A. Agresti, M. Veraar, Annales de l’institut Henri Poincare Probability and Statistics 60 (2024) 413–430. date_created: 2024-03-17T23:00:58Z date_published: 2024-02-01T00:00:00Z date_updated: 2024-03-19T08:14:17Z day: '01' department: - _id: JuFi doi: 10.1214/22-AIHP1333 external_id: arxiv: - '2106.01274' intvolume: ' 60' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2106.01274 month: '02' oa: 1 oa_version: Preprint page: 413-430 publication: Annales de l'institut Henri Poincare Probability and Statistics publication_identifier: issn: - 0246-0203 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 60 year: '2024' ... --- _id: '10550' abstract: - lang: eng text: The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy inequality. The difficulties in establishing global renormalised solutions caused by possibly degenerate diffusion are overcome by introducing a new class of weighted truncation functions. By means of the obtained global renormalised solutions, we study the large-time behaviour of complex balanced systems arising from chemical reaction network theory with non-linear diffusion. When the reaction network does not admit boundary equilibria, the complex balanced equilibrium is shown, by using the entropy method, to exponentially attract all renormalised solutions in the same compatibility class. This convergence extends even to a range of non-linear diffusion, where global existence is an open problem, yet we are able to show that solutions to approximate systems converge exponentially to equilibrium uniformly in the regularisation parameter. acknowledgement: "We thank the referees for their valuable comments and suggestions. A major part of this work was carried out when B. Q. Tang visited the Institute of Science and Technology Austria (ISTA). The hospitality of ISTA is greatly acknowledged. This work was partially supported by NAWI Graz.\r\nOpen access funding provided by University of Graz." article_number: '66' article_processing_charge: No article_type: original author: - first_name: Klemens full_name: Fellner, Klemens last_name: Fellner - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Michael full_name: Kniely, Michael id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87 last_name: Kniely orcid: 0000-0001-5645-4333 - first_name: Bao Quoc full_name: Tang, Bao Quoc last_name: Tang citation: ama: Fellner K, Fischer JL, Kniely M, Tang BQ. Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. 2023;33. doi:10.1007/s00332-023-09926-w apa: Fellner, K., Fischer, J. L., Kniely, M., & Tang, B. Q. (2023). Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-09926-w chicago: Fellner, Klemens, Julian L Fischer, Michael Kniely, and Bao Quoc Tang. “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear Science. Springer Nature, 2023. https://doi.org/10.1007/s00332-023-09926-w. ieee: K. Fellner, J. L. Fischer, M. Kniely, and B. Q. Tang, “Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion,” Journal of Nonlinear Science, vol. 33. Springer Nature, 2023. ista: Fellner K, Fischer JL, Kniely M, Tang BQ. 2023. Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion. Journal of Nonlinear Science. 33, 66. mla: Fellner, Klemens, et al. “Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear Science, vol. 33, 66, Springer Nature, 2023, doi:10.1007/s00332-023-09926-w. short: K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science 33 (2023). date_created: 2021-12-16T12:15:35Z date_published: 2023-06-07T00:00:00Z date_updated: 2023-08-01T14:40:33Z day: '07' ddc: - '510' department: - _id: JuFi doi: 10.1007/s00332-023-09926-w external_id: arxiv: - '2109.12019' isi: - '001002343400002' file: - access_level: open_access checksum: f3f0f0886098e31c81116cff8183750b content_type: application/pdf creator: dernst date_created: 2023-06-19T07:33:53Z date_updated: 2023-06-19T07:33:53Z file_id: '13149' file_name: 2023_JourNonlinearScience_Fellner.pdf file_size: 742315 relation: main_file success: 1 file_date_updated: 2023-06-19T07:33:53Z has_accepted_license: '1' intvolume: ' 33' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: Journal of Nonlinear Science publication_identifier: eissn: - 1432-1467 issn: - 0938-8974 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 33 year: '2023' ... --- _id: '13043' abstract: - lang: eng text: "We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction\r\nof a gradient flow calibration in the sense of the recent work of Fischer et al. (2020) for any such\r\ncluster. This extends the two-dimensional construction to the three-dimensional case of surfaces\r\nmeeting along triple junctions." acknowledgement: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813. article_processing_charge: No article_type: original author: - first_name: Sebastian full_name: Hensel, Sebastian id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87 last_name: Hensel orcid: 0000-0001-7252-8072 - first_name: Tim full_name: Laux, Tim last_name: Laux citation: ama: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. 2023;25(1):37-107. doi:10.4171/IFB/484 apa: Hensel, S., & Laux, T. (2023). Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. EMS Press. https://doi.org/10.4171/IFB/484 chicago: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” Interfaces and Free Boundaries. EMS Press, 2023. https://doi.org/10.4171/IFB/484. ieee: S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow of double bubbles,” Interfaces and Free Boundaries, vol. 25, no. 1. EMS Press, pp. 37–107, 2023. ista: Hensel S, Laux T. 2023. Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. 25(1), 37–107. mla: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” Interfaces and Free Boundaries, vol. 25, no. 1, EMS Press, 2023, pp. 37–107, doi:10.4171/IFB/484. short: S. Hensel, T. Laux, Interfaces and Free Boundaries 25 (2023) 37–107. date_created: 2023-05-21T22:01:06Z date_published: 2023-04-20T00:00:00Z date_updated: 2023-08-01T14:43:29Z day: '20' ddc: - '510' department: - _id: JuFi doi: 10.4171/IFB/484 ec_funded: 1 external_id: arxiv: - '2108.01733' isi: - '000975817300002' file: - access_level: open_access checksum: 622422484810441e48f613e968c7e7a4 content_type: application/pdf creator: dernst date_created: 2023-05-22T07:24:13Z date_updated: 2023-05-22T07:24:13Z file_id: '13045' file_name: 2023_Interfaces_Hensel.pdf file_size: 867876 relation: main_file success: 1 file_date_updated: 2023-05-22T07:24:13Z has_accepted_license: '1' intvolume: ' 25' isi: 1 issue: '1' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 37-107 project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: Interfaces and Free Boundaries publication_identifier: eissn: - 1463-9971 issn: - 1463-9963 publication_status: published publisher: EMS Press quality_controlled: '1' related_material: record: - id: '10013' relation: earlier_version status: public scopus_import: '1' status: public title: Weak-strong uniqueness for the mean curvature flow of double bubbles tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 25 year: '2023' ... --- _id: '13129' abstract: - lang: eng text: "We study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior ahom of a stationary random medium. The latter is described by a coefficient field a(x) generated from a given ensemble ⟨⋅⟩ and the corresponding linear elliptic operator −∇⋅a∇. In line with the theory of homogenization, the method proceeds by computing d=3 correctors (d denoting the space dimension). To be numerically tractable, this computation has to be done on a finite domain: the so-called representative volume element, i.e., a large box with, say, periodic boundary conditions. The main message of this article is: Periodize the ensemble instead of its realizations. By this, we mean that it is better to sample from a suitably periodized ensemble than to periodically extend the restriction of a realization a(x) from the whole-space ensemble ⟨⋅⟩. We make this point by investigating the bias (or systematic error), i.e., the difference between ahom and the expected value of the RVE method, in terms of its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x), we heuristically argue that this error is generically O(L−1). In case of a suitable periodization of ⟨⋅⟩\r\n, we rigorously show that it is O(L−d). In fact, we give a characterization of the leading-order error term for both strategies and argue that even in the isotropic case it is generically non-degenerate. We carry out the rigorous analysis in the convenient setting of ensembles ⟨⋅⟩\r\n of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for optimal stochastic estimates of correctors. We actually need control of second-order correctors to capture the leading-order error term. This is due to inversion symmetry when applying the two-scale expansion to the Green function. As a bonus, we present a stream-lined strategy to estimate the error in a higher-order two-scale expansion of the Green function." acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Nicolas full_name: Clozeau, Nicolas id: fea1b376-906f-11eb-847d-b2c0cf46455b last_name: Clozeau - first_name: Marc full_name: Josien, Marc last_name: Josien - first_name: Felix full_name: Otto, Felix last_name: Otto - first_name: Qiang full_name: Xu, Qiang last_name: Xu citation: ama: 'Clozeau N, Josien M, Otto F, Xu Q. Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics. 2023. doi:10.1007/s10208-023-09613-y' apa: 'Clozeau, N., Josien, M., Otto, F., & Xu, Q. (2023). Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics. Springer Nature. https://doi.org/10.1007/s10208-023-09613-y' chicago: 'Clozeau, Nicolas, Marc Josien, Felix Otto, and Qiang Xu. “Bias in the Representative Volume Element Method: Periodize the Ensemble Instead of Its Realizations.” Foundations of Computational Mathematics. Springer Nature, 2023. https://doi.org/10.1007/s10208-023-09613-y.' ieee: 'N. Clozeau, M. Josien, F. Otto, and Q. Xu, “Bias in the representative volume element method: Periodize the ensemble instead of its realizations,” Foundations of Computational Mathematics. Springer Nature, 2023.' ista: 'Clozeau N, Josien M, Otto F, Xu Q. 2023. Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics.' mla: 'Clozeau, Nicolas, et al. “Bias in the Representative Volume Element Method: Periodize the Ensemble Instead of Its Realizations.” Foundations of Computational Mathematics, Springer Nature, 2023, doi:10.1007/s10208-023-09613-y.' short: N. Clozeau, M. Josien, F. Otto, Q. Xu, Foundations of Computational Mathematics (2023). date_created: 2023-06-11T22:00:40Z date_published: 2023-05-30T00:00:00Z date_updated: 2023-08-02T06:12:39Z day: '30' ddc: - '510' department: - _id: JuFi doi: 10.1007/s10208-023-09613-y external_id: isi: - '000999623100001' has_accepted_license: '1' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s10208-023-09613-y month: '05' oa: 1 oa_version: Published Version publication: Foundations of Computational Mathematics publication_identifier: eissn: - 1615-3383 issn: - 1615-3375 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: 'Bias in the representative volume element method: Periodize the ensemble instead of its realizations' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2023' ... --- _id: '10173' abstract: - lang: eng text: We study the large scale behavior of elliptic systems with stationary random coefficient that have only slowly decaying correlations. To this aim we analyze the so-called corrector equation, a degenerate elliptic equation posed in the probability space. In this contribution, we use a parabolic approach and optimally quantify the time decay of the semigroup. For the theoretical point of view, we prove an optimal decay estimate of the gradient and flux of the corrector when spatially averaged over a scale R larger than 1. For the numerical point of view, our results provide convenient tools for the analysis of various numerical methods. acknowledgement: "I would like to thank my advisor Antoine Gloria for suggesting this problem to me, as well for many interesting discussions and suggestions.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria)." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Nicolas full_name: Clozeau, Nicolas id: fea1b376-906f-11eb-847d-b2c0cf46455b last_name: Clozeau citation: ama: 'Clozeau N. Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. 2023;11:1254–1378. doi:10.1007/s40072-022-00254-w' apa: 'Clozeau, N. (2023). Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-022-00254-w' chicago: 'Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization  for Correlated Coefficient Fields.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2023. https://doi.org/10.1007/s40072-022-00254-w.' ieee: 'N. Clozeau, “Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 11. Springer Nature, pp. 1254–1378, 2023.' ista: 'Clozeau N. 2023. Optimal decay of the parabolic semigroup in stochastic homogenization  for correlated coefficient fields. Stochastics and Partial Differential Equations: Analysis and Computations. 11, 1254–1378.' mla: 'Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic Homogenization  for Correlated Coefficient Fields.” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 11, Springer Nature, 2023, pp. 1254–1378, doi:10.1007/s40072-022-00254-w.' short: 'N. Clozeau, Stochastics and Partial Differential Equations: Analysis and Computations 11 (2023) 1254–1378.' date_created: 2021-10-23T10:50:22Z date_published: 2023-09-01T00:00:00Z date_updated: 2023-08-14T11:51:47Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1007/s40072-022-00254-w external_id: arxiv: - '2102.07452' isi: - '000799715600001' file: - access_level: open_access checksum: f83dcaecdbd3ace862c4ed97a20e8501 content_type: application/pdf creator: dernst date_created: 2023-08-14T11:51:04Z date_updated: 2023-08-14T11:51:04Z file_id: '14052' file_name: 2023_StochPartialDiffEquations_Clozeau.pdf file_size: 1635193 relation: main_file success: 1 file_date_updated: 2023-08-14T11:51:04Z has_accepted_license: '1' intvolume: ' 11' isi: 1 language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 1254–1378 publication: 'Stochastics and Partial Differential Equations: Analysis and Computations' publication_identifier: issn: - 2194-0401 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 11 year: '2023' ... --- _id: '12429' abstract: - lang: eng text: In this paper, we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity problems for fractional evolution equations and stochastic evolution equations, where uniform trace estimates on the half-line are shown. acknowledgement: The first author has been partially supported by the Nachwuchsring—Network for the promotion of young scientists—at TU Kaiserslautern. The second and third authors were supported by the Vidi subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO). article_processing_charge: No article_type: original author: - first_name: Antonio full_name: Agresti, Antonio id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72 last_name: Agresti orcid: 0000-0002-9573-2962 - first_name: Nick full_name: Lindemulder, Nick last_name: Lindemulder - first_name: Mark full_name: Veraar, Mark last_name: Veraar citation: ama: Agresti A, Lindemulder N, Veraar M. On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. 2023;296(4):1319-1350. doi:10.1002/mana.202100192 apa: Agresti, A., Lindemulder, N., & Veraar, M. (2023). On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. Wiley. https://doi.org/10.1002/mana.202100192 chicago: Agresti, Antonio, Nick Lindemulder, and Mark Veraar. “On the Trace Embedding and Its Applications to Evolution Equations.” Mathematische Nachrichten. Wiley, 2023. https://doi.org/10.1002/mana.202100192. ieee: A. Agresti, N. Lindemulder, and M. Veraar, “On the trace embedding and its applications to evolution equations,” Mathematische Nachrichten, vol. 296, no. 4. Wiley, pp. 1319–1350, 2023. ista: Agresti A, Lindemulder N, Veraar M. 2023. On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. 296(4), 1319–1350. mla: Agresti, Antonio, et al. “On the Trace Embedding and Its Applications to Evolution Equations.” Mathematische Nachrichten, vol. 296, no. 4, Wiley, 2023, pp. 1319–50, doi:10.1002/mana.202100192. short: A. Agresti, N. Lindemulder, M. Veraar, Mathematische Nachrichten 296 (2023) 1319–1350. date_created: 2023-01-29T23:00:59Z date_published: 2023-04-01T00:00:00Z date_updated: 2023-08-16T11:41:42Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1002/mana.202100192 external_id: arxiv: - '2104.05063' isi: - '000914134900001' file: - access_level: open_access checksum: 6f099f1d064173784d1a27716a2cc795 content_type: application/pdf creator: dernst date_created: 2023-08-16T11:40:02Z date_updated: 2023-08-16T11:40:02Z file_id: '14067' file_name: 2023_MathNachrichten_Agresti.pdf file_size: 449280 relation: main_file success: 1 file_date_updated: 2023-08-16T11:40:02Z has_accepted_license: '1' intvolume: ' 296' isi: 1 issue: '4' language: - iso: eng license: https://creativecommons.org/licenses/by-nc/4.0/ month: '04' oa: 1 oa_version: Published Version page: 1319-1350 publication: Mathematische Nachrichten publication_identifier: eissn: - 1522-2616 issn: - 0025-584X publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: On the trace embedding and its applications to evolution equations tmp: image: /images/cc_by_nc.png legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) short: CC BY-NC (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 296 year: '2023' ... --- _id: '14451' abstract: - lang: eng text: 'We investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT, XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of the proposed Multi-Objective algorithm, and provide preliminary statistical evidence showing increased predictive stability over the corresponding Single-Objective strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge over the corresponding Single-Objective strategy when the reward mechanism is sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss the generalization properties with respect to the discount factor. The entirety of our code is provided in open-source format.' acknowledgement: Open access funding provided by Università degli Studi di Trieste within the CRUI-CARE Agreement. Funding was provided by Austrian Science Fund (Grant No. F65), Horizon 2020 (Grant No. 754411) and Österreichische Forschungsförderungsgesellschaft. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Federico full_name: Cornalba, Federico id: 2CEB641C-A400-11E9-A717-D712E6697425 last_name: Cornalba orcid: 0000-0002-6269-5149 - first_name: Constantin full_name: Disselkamp, Constantin last_name: Disselkamp - first_name: Davide full_name: Scassola, Davide last_name: Scassola - first_name: Christopher full_name: Helf, Christopher last_name: Helf citation: ama: 'Cornalba F, Disselkamp C, Scassola D, Helf C. Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications. 2023. doi:10.1007/s00521-023-09033-7' apa: 'Cornalba, F., Disselkamp, C., Scassola, D., & Helf, C. (2023). Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications. Springer Nature. https://doi.org/10.1007/s00521-023-09033-7' chicago: 'Cornalba, Federico, Constantin Disselkamp, Davide Scassola, and Christopher Helf. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” Neural Computing and Applications. Springer Nature, 2023. https://doi.org/10.1007/s00521-023-09033-7.' ieee: 'F. Cornalba, C. Disselkamp, D. Scassola, and C. Helf, “Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading,” Neural Computing and Applications. Springer Nature, 2023.' ista: 'Cornalba F, Disselkamp C, Scassola D, Helf C. 2023. Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications.' mla: 'Cornalba, Federico, et al. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” Neural Computing and Applications, Springer Nature, 2023, doi:10.1007/s00521-023-09033-7.' short: F. Cornalba, C. Disselkamp, D. Scassola, C. Helf, Neural Computing and Applications (2023). date_created: 2023-10-22T22:01:16Z date_published: 2023-10-05T00:00:00Z date_updated: 2023-10-31T10:58:28Z day: '05' department: - _id: JuFi doi: 10.1007/s00521-023-09033-7 ec_funded: 1 external_id: arxiv: - '2203.04579' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00521-023-09033-7 month: '10' oa: 1 oa_version: Published Version project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Neural Computing and Applications publication_identifier: eissn: - 1433-3058 issn: - 0941-0643 publication_status: epub_ahead publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: 'Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '14554' abstract: - lang: eng text: 'The Regularised Inertial Dean–Kawasaki model (RIDK) – introduced by the authors and J. Zimmer in earlier works – is a nonlinear stochastic PDE capturing fluctuations around the meanfield limit for large-scale particle systems in both particle density and momentum density. We focus on the following two aspects. Firstly, we set up a Discontinuous Galerkin (DG) discretisation scheme for the RIDK model: we provide suitable definitions of numerical fluxes at the interface of the mesh elements which are consistent with the wave-type nature of the RIDK model and grant stability of the simulations, and we quantify the rate of convergence in mean square to the continuous RIDK model. Secondly, we introduce modifications of the RIDK model in order to preserve positivity of the density (such a feature only holds in a “high-probability sense” for the original RIDK model). By means of numerical simulations, we show that the modifications lead to physically realistic and positive density profiles. In one case, subject to additional regularity constraints, we also prove positivity. Finally, we present an application of our methodology to a system of diffusing and reacting particles. Our Python code is available in open-source format.' acknowledgement: "The authors thank the anonymous referees for their careful reading of the manuscript and their\r\nvaluable suggestions. FC gratefully acknowledges funding from the Austrian Science Fund (FWF) through the project F65, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 754411 (the latter funding source covered the first part of this project)." article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Federico full_name: Cornalba, Federico id: 2CEB641C-A400-11E9-A717-D712E6697425 last_name: Cornalba orcid: 0000-0002-6269-5149 - first_name: Tony full_name: Shardlow, Tony last_name: Shardlow citation: ama: 'Cornalba F, Shardlow T. The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis. 2023;57(5):3061-3090. doi:10.1051/m2an/2023077' apa: 'Cornalba, F., & Shardlow, T. (2023). The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences. https://doi.org/10.1051/m2an/2023077' chicago: 'Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’ Kawasaki Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density Regime.” ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences, 2023. https://doi.org/10.1051/m2an/2023077.' ieee: 'F. Cornalba and T. Shardlow, “The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime,” ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57, no. 5. EDP Sciences, pp. 3061–3090, 2023.' ista: 'Cornalba F, Shardlow T. 2023. The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis. 57(5), 3061–3090.' mla: 'Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’ Kawasaki Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density Regime.” ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57, no. 5, EDP Sciences, 2023, pp. 3061–90, doi:10.1051/m2an/2023077.' short: 'F. Cornalba, T. Shardlow, ESAIM: Mathematical Modelling and Numerical Analysis 57 (2023) 3061–3090.' date_created: 2023-11-19T23:00:55Z date_published: 2023-09-01T00:00:00Z date_updated: 2023-11-20T08:38:47Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1051/m2an/2023077 ec_funded: 1 file: - access_level: open_access checksum: 3aef1475b1882c8dec112df9a5167c39 content_type: application/pdf creator: dernst date_created: 2023-11-20T08:34:57Z date_updated: 2023-11-20T08:34:57Z file_id: '14560' file_name: 2023_ESAIM_Cornalba.pdf file_size: 1508534 relation: main_file success: 1 file_date_updated: 2023-11-20T08:34:57Z has_accepted_license: '1' intvolume: ' 57' issue: '5' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 3061-3090 project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 'ESAIM: Mathematical Modelling and Numerical Analysis' publication_identifier: eissn: - 2804-7214 issn: - 2822-7840 publication_status: published publisher: EDP Sciences quality_controlled: '1' related_material: link: - relation: software url: https://github.com/tonyshardlow/RIDK-FD scopus_import: '1' status: public title: 'The regularised inertial Dean'' Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 57 year: '2023' ... --- _id: '14042' abstract: - lang: eng text: Long-time and large-data existence of weak solutions for initial- and boundary-value problems concerning three-dimensional flows of incompressible fluids is nowadays available not only for Navier–Stokes fluids but also for various fluid models where the relation between the Cauchy stress tensor and the symmetric part of the velocity gradient is nonlinear. The majority of such studies however concerns models where such a dependence is explicit (the stress is a function of the velocity gradient), which makes the class of studied models unduly restrictive. The same concerns boundary conditions, or more precisely the slipping mechanisms on the boundary, where the no-slip is still the most preferred condition considered in the literature. Our main objective is to develop a robust mathematical theory for unsteady internal flows of implicitly constituted incompressible fluids with implicit relations between the tangential projections of the velocity and the normal traction on the boundary. The theory covers numerous rheological models used in chemistry, biorheology, polymer and food industry as well as in geomechanics. It also includes, as special cases, nonlinear slip as well as stick–slip boundary conditions. Unlike earlier studies, the conditions characterizing admissible classes of constitutive equations are expressed by means of tools of elementary calculus. In addition, a fully constructive proof (approximation scheme) is incorporated. Finally, we focus on the question of uniqueness of such weak solutions. acknowledgement: "M. Bulíček and J. Málek acknowledge the support of the project No. 20-11027X financed by the Czech Science foundation (GAČR). M. Bulíček and J. Málek are members of the Nečas Center for Mathematical Modelling.\r\nOpen access publishing supported by the National Technical Library in Prague." article_number: '72' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Miroslav full_name: Bulíček, Miroslav last_name: Bulíček - first_name: Josef full_name: Málek, Josef last_name: Málek - first_name: Erika full_name: Maringová, Erika id: dbabca31-66eb-11eb-963a-fb9c22c880b4 last_name: Maringová citation: ama: Bulíček M, Málek J, Maringová E. On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. Journal of Mathematical Fluid Mechanics. 2023;25(3). doi:10.1007/s00021-023-00803-w apa: Bulíček, M., Málek, J., & Maringová, E. (2023). On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. Journal of Mathematical Fluid Mechanics. Springer Nature. https://doi.org/10.1007/s00021-023-00803-w chicago: Bulíček, Miroslav, Josef Málek, and Erika Maringová. “On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary.” Journal of Mathematical Fluid Mechanics. Springer Nature, 2023. https://doi.org/10.1007/s00021-023-00803-w. ieee: M. Bulíček, J. Málek, and E. Maringová, “On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary,” Journal of Mathematical Fluid Mechanics, vol. 25, no. 3. Springer Nature, 2023. ista: Bulíček M, Málek J, Maringová E. 2023. On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. Journal of Mathematical Fluid Mechanics. 25(3), 72. mla: Bulíček, Miroslav, et al. “On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary.” Journal of Mathematical Fluid Mechanics, vol. 25, no. 3, 72, Springer Nature, 2023, doi:10.1007/s00021-023-00803-w. short: M. Bulíček, J. Málek, E. Maringová, Journal of Mathematical Fluid Mechanics 25 (2023). date_created: 2023-08-13T22:01:13Z date_published: 2023-08-01T00:00:00Z date_updated: 2023-12-13T12:08:08Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1007/s00021-023-00803-w external_id: arxiv: - '2301.12834' isi: - '001040354900001' file: - access_level: open_access checksum: c549cd8f0dd02ed60477a05ca045f481 content_type: application/pdf creator: dernst date_created: 2023-08-14T07:24:17Z date_updated: 2023-08-14T07:24:17Z file_id: '14046' file_name: 2023_JourMathFluidMech_Bulicek.pdf file_size: 845748 relation: main_file success: 1 file_date_updated: 2023-08-14T07:24:17Z has_accepted_license: '1' intvolume: ' 25' isi: 1 issue: '3' language: - iso: eng month: '08' oa: 1 oa_version: Published Version publication: Journal of Mathematical Fluid Mechanics publication_identifier: eissn: - 1422-6952 issn: - 1422-6928 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 25 year: '2023' ... --- _id: '12486' abstract: - lang: eng text: This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we prove that a suitable multiplicative noise of transport type has a regularizing effect. More precisely, for both a sufficiently noise intensity and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary large time. Global existence is shown for the case of exponentially decreasing mass. The proofs combine and extend recent developments in regularization by noise and in the Lp(Lq)-approach to stochastic PDEs, highlighting new connections between the two areas. acknowledgement: "The author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 948819).\r\nThe author thanks Lorenzo Dello Schiavo, Lucio Galeati and Mark Veraar for helpful comments. The author acknowledges Caterina Balzotti for her support in creating the picture. The author\r\nthanks the anonymous referee for helpful comments. " article_processing_charge: No article_type: original author: - first_name: Antonio full_name: Agresti, Antonio id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72 last_name: Agresti orcid: 0000-0002-9573-2962 citation: ama: 'Agresti A. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations. 2023. doi:10.1007/s40072-023-00319-4' apa: 'Agresti, A. (2023). Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-023-00319-4' chicago: 'Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2023. https://doi.org/10.1007/s40072-023-00319-4.' ieee: 'A. Agresti, “Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations,” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2023.' ista: 'Agresti A. 2023. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations.' mla: 'Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” Stochastics and Partial Differential Equations: Analysis and Computations, Springer Nature, 2023, doi:10.1007/s40072-023-00319-4.' short: 'A. Agresti, Stochastics and Partial Differential Equations: Analysis and Computations (2023).' date_created: 2023-02-02T10:45:47Z date_published: 2023-11-28T00:00:00Z date_updated: 2023-12-18T07:53:45Z day: '28' ddc: - '510' department: - _id: JuFi doi: 10.1007/s40072-023-00319-4 ec_funded: 1 external_id: arxiv: - '2207.08293' has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s40072-023-00319-4 month: '11' oa: 1 oa_version: Submitted Version project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: 'Stochastics and Partial Differential Equations: Analysis and Computations' publication_identifier: eissn: - 2194-041X issn: - 2194-0401 publication_status: epub_ahead publisher: Springer Nature scopus_import: '1' status: public title: Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '14755' abstract: - lang: eng text: We consider the sharp interface limit for the scalar-valued and vector-valued Allen–Cahn equation with homogeneous Neumann boundary condition in a bounded smooth domain Ω of arbitrary dimension N ⩾ 2 in the situation when a two-phase diffuse interface has developed and intersects the boundary ∂ Ω. The limit problem is mean curvature flow with 90°-contact angle and we show convergence in strong norms for well-prepared initial data as long as a smooth solution to the limit problem exists. To this end we assume that the limit problem has a smooth solution on [ 0 , T ] for some time T > 0. Based on the latter we construct suitable curvilinear coordinates and set up an asymptotic expansion for the scalar-valued and the vector-valued Allen–Cahn equation. In order to estimate the difference of the exact and approximate solutions with a Gronwall-type argument, a spectral estimate for the linearized Allen–Cahn operator in both cases is required. The latter will be shown in a separate paper, cf. (Moser (2021)). acknowledgement: "The author gratefully acknowledges support through DFG, GRK 1692 “Curvature,\r\nCycles and Cohomology” during parts of the work." article_processing_charge: No article_type: original author: - first_name: Maximilian full_name: Moser, Maximilian id: a60047a9-da77-11eb-85b4-c4dc385ebb8c last_name: Moser citation: ama: 'Moser M. Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. 2023;131(3-4):297-383. doi:10.3233/asy-221775' apa: 'Moser, M. (2023). Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. IOS Press. https://doi.org/10.3233/asy-221775' chicago: 'Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part I: Convergence Result.” Asymptotic Analysis. IOS Press, 2023. https://doi.org/10.3233/asy-221775.' ieee: 'M. Moser, “Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result,” Asymptotic Analysis, vol. 131, no. 3–4. IOS Press, pp. 297–383, 2023.' ista: 'Moser M. 2023. Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result. Asymptotic Analysis. 131(3–4), 297–383.' mla: 'Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part I: Convergence Result.” Asymptotic Analysis, vol. 131, no. 3–4, IOS Press, 2023, pp. 297–383, doi:10.3233/asy-221775.' short: M. Moser, Asymptotic Analysis 131 (2023) 297–383. date_created: 2024-01-08T13:13:28Z date_published: 2023-02-02T00:00:00Z date_updated: 2024-01-09T09:22:16Z day: '02' department: - _id: JuFi doi: 10.3233/asy-221775 external_id: arxiv: - '2105.07100' intvolume: ' 131' issue: 3-4 keyword: - General Mathematics language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2105.07100 month: '02' oa: 1 oa_version: Preprint page: 297-383 publication: Asymptotic Analysis publication_identifier: eissn: - 1875-8576 issn: - 0921-7134 publication_status: published publisher: IOS Press quality_controlled: '1' scopus_import: '1' status: public title: 'Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 131 year: '2023' ... --- _id: '14661' abstract: - lang: eng text: 'This paper is concerned with equilibrium configurations of one-dimensional particle systems with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its passage to the continuum. The goal is to derive compactness results for a Γ-development of the energy with the novelty that external forces are allowed. In particular, the forces may depend on Lagrangian or Eulerian coordinates and thus may model dead as well as live loads. Our result is based on a new technique for deriving compactness results which are required for calculating the first-order Γ-limit in the presence of external forces: instead of comparing a configuration of n atoms to a global minimizer of the Γ-limit, we compare the configuration to a minimizer in some subclass of functions which in some sense are "close to" the configuration. The paper is complemented with the study of the minimizers of the Γ-limit.' article_processing_charge: No article_type: original author: - first_name: Marcello full_name: Carioni, Marcello last_name: Carioni - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Anja full_name: Schlömerkemper, Anja last_name: Schlömerkemper citation: ama: 'Carioni M, Fischer JL, Schlömerkemper A. External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development. Journal of Convex Analysis. 2023;30(1):217-247.' apa: 'Carioni, M., Fischer, J. L., & Schlömerkemper, A. (2023). External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development. Journal of Convex Analysis. Heldermann Verlag.' chicago: 'Carioni, Marcello, Julian L Fischer, and Anja Schlömerkemper. “External Forces in the Continuum Limit of Discrete Systems with Non-Convex Interaction Potentials: Compactness for a Γ-Development.” Journal of Convex Analysis. Heldermann Verlag, 2023.' ieee: 'M. Carioni, J. L. Fischer, and A. Schlömerkemper, “External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development,” Journal of Convex Analysis, vol. 30, no. 1. Heldermann Verlag, pp. 217–247, 2023.' ista: 'Carioni M, Fischer JL, Schlömerkemper A. 2023. External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development. Journal of Convex Analysis. 30(1), 217–247.' mla: 'Carioni, Marcello, et al. “External Forces in the Continuum Limit of Discrete Systems with Non-Convex Interaction Potentials: Compactness for a Γ-Development.” Journal of Convex Analysis, vol. 30, no. 1, Heldermann Verlag, 2023, pp. 217–47.' short: M. Carioni, J.L. Fischer, A. Schlömerkemper, Journal of Convex Analysis 30 (2023) 217–247. date_created: 2023-12-10T23:00:59Z date_published: 2023-01-01T00:00:00Z date_updated: 2024-01-16T12:03:05Z day: '01' department: - _id: JuFi external_id: arxiv: - '1811.09857' isi: - '001115503400013' intvolume: ' 30' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1811.09857 month: '01' oa: 1 oa_version: Preprint page: 217-247 publication: Journal of Convex Analysis publication_identifier: eissn: - 2363-6394 issn: - 0944-6532 publication_status: published publisher: Heldermann Verlag quality_controlled: '1' scopus_import: '1' status: public title: 'External forces in the continuum limit of discrete systems with non-convex interaction potentials: Compactness for a Γ-development' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 30 year: '2023' ... --- _id: '13135' abstract: - lang: eng text: In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model. acknowledgement: The first author has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 948819) Image 1. The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO). article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Antonio full_name: Agresti, Antonio id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72 last_name: Agresti orcid: 0000-0002-9573-2962 - first_name: Mark full_name: Veraar, Mark last_name: Veraar citation: ama: 'Agresti A, Veraar M. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. 2023;368(9):247-300. doi:10.1016/j.jde.2023.05.038' apa: 'Agresti, A., & Veraar, M. (2023). Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2023.05.038' chicago: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” Journal of Differential Equations. Elsevier, 2023. https://doi.org/10.1016/j.jde.2023.05.038.' ieee: 'A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity,” Journal of Differential Equations, vol. 368, no. 9. Elsevier, pp. 247–300, 2023.' ista: 'Agresti A, Veraar M. 2023. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. 368(9), 247–300.' mla: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” Journal of Differential Equations, vol. 368, no. 9, Elsevier, 2023, pp. 247–300, doi:10.1016/j.jde.2023.05.038.' short: A. Agresti, M. Veraar, Journal of Differential Equations 368 (2023) 247–300. date_created: 2023-06-18T22:00:45Z date_published: 2023-09-25T00:00:00Z date_updated: 2024-01-29T11:04:41Z day: '25' ddc: - '510' department: - _id: JuFi doi: 10.1016/j.jde.2023.05.038 ec_funded: 1 external_id: isi: - '001019018700001' file: - access_level: open_access checksum: 246b703b091dfe047bfc79abf0891a63 content_type: application/pdf creator: dernst date_created: 2024-01-29T11:03:09Z date_updated: 2024-01-29T11:03:09Z file_id: '14895' file_name: 2023_JourDifferentialEquations_Agresti.pdf file_size: 834638 relation: main_file success: 1 file_date_updated: 2024-01-29T11:03:09Z has_accepted_license: '1' intvolume: ' 368' isi: 1 issue: '9' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 247-300 project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication: Journal of Differential Equations publication_identifier: eissn: - 1090-2732 issn: - 0022-0396 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: 'Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 368 year: '2023' ... --- _id: '10551' abstract: - lang: eng text: 'The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuations of the density of N independent diffusing particles in the regime of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation presents a substantial challenge for both its analysis and its rigorous mathematical justification. Besides being non-renormalisable by the theory of regularity structures by Hairer et al., it has recently been shown to not even admit nontrivial martingale solutions. In the present work, we give a rigorous and fully quantitative justification of the Dean–Kawasaki equation by considering the natural regularisation provided by standard numerical discretisations: We show that structure-preserving discretisations of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting diffusing particles to arbitrary order in N−1 (in suitable weak metrics). In other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate and efficient numerical simulations of the density fluctuations of independent diffusing particles.' acknowledgement: "We thank the anonymous referee for his/her careful reading of the manuscript and valuable suggestions. FC gratefully acknowledges funding from the Austrian Science Fund (FWF) through the project F65, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.\r\nOpen access funding provided by Austrian Science Fund (FWF)." article_number: '76' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Federico full_name: Cornalba, Federico id: 2CEB641C-A400-11E9-A717-D712E6697425 last_name: Cornalba orcid: 0000-0002-6269-5149 - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X citation: ama: Cornalba F, Fischer JL. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. 2023;247(5). doi:10.1007/s00205-023-01903-7 apa: Cornalba, F., & Fischer, J. L. (2023). The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-023-01903-7 chicago: Cornalba, Federico, and Julian L Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive for Rational Mechanics and Analysis. Springer Nature, 2023. https://doi.org/10.1007/s00205-023-01903-7. ieee: F. Cornalba and J. L. Fischer, “The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles,” Archive for Rational Mechanics and Analysis, vol. 247, no. 5. Springer Nature, 2023. ista: Cornalba F, Fischer JL. 2023. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. 247(5), 76. mla: Cornalba, Federico, and Julian L. Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive for Rational Mechanics and Analysis, vol. 247, no. 5, 76, Springer Nature, 2023, doi:10.1007/s00205-023-01903-7. short: F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247 (2023). date_created: 2021-12-16T12:16:03Z date_published: 2023-08-04T00:00:00Z date_updated: 2024-01-30T12:10:10Z day: '04' ddc: - '510' department: - _id: JuFi doi: 10.1007/s00205-023-01903-7 ec_funded: 1 external_id: arxiv: - '2109.06500' isi: - '001043086800001' file: - access_level: open_access checksum: 4529eeff170b6745a461d397ee611b5a content_type: application/pdf creator: dernst date_created: 2024-01-30T12:09:34Z date_updated: 2024-01-30T12:09:34Z file_id: '14904' file_name: 2023_ArchiveRationalMech_Cornalba.pdf file_size: 1851185 relation: main_file success: 1 file_date_updated: 2024-01-30T12:09:34Z has_accepted_license: '1' intvolume: ' 247' isi: 1 issue: '5' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: Archive for Rational Mechanics and Analysis publication_identifier: eissn: - 1432-0673 issn: - 0003-9527 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 247 year: '2023' ... --- _id: '14587' abstract: - lang: eng text: "This thesis concerns the application of variational methods to the study of evolution problems arising in fluid mechanics and in material sciences. The main focus is on weak-strong stability properties of some curvature driven interface evolution problems, such as the two-phase Navier–Stokes flow with surface tension and multiphase mean curvature flow, and on the phase-field approximation of the latter. Furthermore, we discuss a variational approach to the study of a class of doubly nonlinear wave equations.\r\nFirst, we consider the two-phase Navier–Stokes flow with surface tension within a bounded domain. The two fluids are immiscible and separated by a sharp interface, which intersects the boundary of the domain at a constant contact angle of ninety degree. We devise a suitable concept of varifolds solutions for the associated interface evolution problem and we establish a weak-strong uniqueness principle in case of a two dimensional ambient space. In order to focus on the boundary effects and on the singular geometry of the evolving domains, we work for simplicity in the regime of same viscosities for the two fluids.\r\nThe core of the thesis consists in the rigorous proof of the convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow for a suitable class of multi- well potentials and for well-prepared initial data. We even establish a rate of convergence. Our relative energy approach relies on the concept of gradient-flow calibration for branching singularities in multiphase mean curvature flow and thus enables us to overcome the limitations of other approaches. To the best of the author’s knowledge, our result is the first quantitative and unconditional one available in the literature for the vectorial/multiphase setting.\r\nThis thesis also contains a first study of weak-strong stability for planar multiphase mean curvature flow beyond the singularity resulting from a topology change. Previous weak-strong results are indeed limited to time horizons before the first topology change of the strong solution. We consider circular topology changes and we prove weak-strong stability for BV solutions to planar multiphase mean curvature flow beyond the associated singular times by dynamically adapting the strong solutions to the weak one by means of a space-time shift.\r\nIn the context of interface evolution problems, our proofs for the main results of this thesis are based on the relative energy technique, relying on novel suitable notions of relative energy functionals, which in particular measure the interface error. Our statements follow from the resulting stability estimates for the relative energy associated to the problem.\r\nAt last, we introduce a variational approach to the study of nonlinear evolution problems. This approach hinges on the minimization of a parameter dependent family of convex functionals over entire trajectories, known as Weighted Inertia-Dissipation-Energy (WIDE) functionals. We consider a class of doubly nonlinear wave equations and establish the convergence, up to subsequences, of the associated WIDE minimizers to a solution of the target problem as the parameter goes to zero." acknowledgement: The research projects contained in this thesis have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819). alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Alice full_name: Marveggio, Alice id: 25647992-AA84-11E9-9D75-8427E6697425 last_name: Marveggio citation: ama: Marveggio A. Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. 2023. doi:10.15479/at:ista:14587 apa: Marveggio, A. (2023). Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14587 chicago: Marveggio, Alice. “Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14587. ieee: A. Marveggio, “Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences,” Institute of Science and Technology Austria, 2023. ista: Marveggio A. 2023. Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. Institute of Science and Technology Austria. mla: Marveggio, Alice. Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14587. short: A. Marveggio, Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences, Institute of Science and Technology Austria, 2023. date_created: 2023-11-21T11:41:05Z date_published: 2023-11-21T00:00:00Z date_updated: 2024-03-22T13:21:28Z day: '21' ddc: - '515' degree_awarded: PhD department: - _id: GradSch - _id: JuFi doi: 10.15479/at:ista:14587 ec_funded: 1 file: - access_level: open_access checksum: 6c7db4cc86da6cdc79f7f358dc7755d4 content_type: application/pdf creator: amarvegg date_created: 2023-11-29T09:09:31Z date_updated: 2023-11-29T09:09:31Z file_id: '14626' file_name: thesis_Marveggio.pdf file_size: 2881100 relation: main_file success: 1 - access_level: closed checksum: 52f28bdf95ec82cff39f3685f9c48e7d content_type: application/zip creator: amarvegg date_created: 2023-11-29T09:10:19Z date_updated: 2024-03-20T12:28:32Z file_id: '14627' file_name: Thesis_Marveggio.zip file_size: 10189696 relation: source_file file_date_updated: 2024-03-20T12:28:32Z has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-sa/4.0/ month: '11' oa: 1 oa_version: Published Version page: '228' project: - _id: 0aa76401-070f-11eb-9043-b5bb049fa26d call_identifier: H2020 grant_number: '948819' name: Bridging Scales in Random Materials publication_identifier: issn: - 2663 - 337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '11842' relation: part_of_dissertation status: public - id: '14597' relation: part_of_dissertation status: public status: public supervisor: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X title: Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2023' ... --- _id: '14772' abstract: - lang: eng text: "Many coupled evolution equations can be described via 2×2-block operator matrices of the form A=[ \r\nA\tB\r\nC\tD\r\n ] in a product space X=X1×X2 with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator A can be seen as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D) though with possibly large relative bound. For such operators the properties of sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time dependent parabolic problem associated with A can be analyzed in maximal Lpt\r\n-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model." acknowledgement: "We would like to thank Tim Binz, Emiel Lorist and Mark Veraar for valuable discussions. We also thank the anonymous referees for their helpful comments and suggestions, and for the very accurate reading of the manuscript.\r\nThe first author has been supported partially by the Nachwuchsring – Network for the promotion of young scientists – at TU Kaiserslautern. Both authors have been supported by MathApp – Mathematics Applied to Real-World Problems - part of the Research Initiative of the Federal State of Rhineland-Palatinate, Germany." article_number: '110146' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Antonio full_name: Agresti, Antonio id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72 last_name: Agresti orcid: 0000-0002-9573-2962 - first_name: Amru full_name: Hussein, Amru last_name: Hussein citation: ama: Agresti A, Hussein A. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. 2023;285(11). doi:10.1016/j.jfa.2023.110146 apa: Agresti, A., & Hussein, A. (2023). Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.110146 chicago: Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.110146. ieee: A. Agresti and A. Hussein, “Maximal Lp-regularity and H∞-calculus for block operator matrices and applications,” Journal of Functional Analysis, vol. 285, no. 11. Elsevier, 2023. ista: Agresti A, Hussein A. 2023. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. 285(11), 110146. mla: Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” Journal of Functional Analysis, vol. 285, no. 11, 110146, Elsevier, 2023, doi:10.1016/j.jfa.2023.110146. short: A. Agresti, A. Hussein, Journal of Functional Analysis 285 (2023). date_created: 2024-01-10T09:15:18Z date_published: 2023-12-01T00:00:00Z date_updated: 2024-03-25T11:37:14Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1016/j.jfa.2023.110146 external_id: arxiv: - '2108.01962' isi: - '001081809000001' file: - access_level: open_access checksum: eda98ca2aa73da91bd074baed34c2b3c content_type: application/pdf creator: dernst date_created: 2024-01-10T11:23:57Z date_updated: 2024-01-10T11:23:57Z file_id: '14789' file_name: 2023_JourFunctionalAnalysis_Agresti.pdf file_size: 1120592 relation: main_file success: 1 file_date_updated: 2024-01-10T11:23:57Z has_accepted_license: '1' intvolume: ' 285' isi: 1 issue: '11' keyword: - Analysis language: - iso: eng month: '12' oa: 1 oa_version: Published Version publication: Journal of Functional Analysis publication_identifier: issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Maximal Lp-regularity and H∞-calculus for block operator matrices and applications tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 285 year: '2023' ...