--- _id: '11858' abstract: - lang: eng text: "This paper is a continuation of Part I of this project, where we developed a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian noise. In the current Part II we consider blow-up criteria and regularization phenomena. As in Part I we can allow nonlinearities with polynomial growth and rough initial values from critical spaces. In the first main result we obtain several new blow-up criteria for quasi- and semilinear stochastic evolution equations. In particular, for semilinear equations we obtain a Serrin type blow-up criterium, which extends a recent result of Prüss–Simonett–Wilke (J Differ Equ 264(3):2028–2074, 2018) to the stochastic setting. Blow-up criteria can be used to prove global well-posedness for SPDEs. As in Part I, maximal regularity techniques and weights in time play a central role in the proofs. Our second contribution is a new method to bootstrap Sobolev and Hölder regularity in time and space, which does not require smoothness of the initial data. The blow-up criteria are at the basis of these new methods. Moreover, in applications the bootstrap results can be combined with our blow-up criteria, to obtain efficient ways to prove global existence. This gives new results even in classical \U0001D43F2-settings, which we illustrate for a concrete SPDE. In future works in preparation we apply the results of the current paper to obtain global well-posedness results and regularity for several concrete SPDEs. These include stochastic Navier–Stokes equations, reaction– diffusion equations and the Allen–Cahn equation. Our setting allows to put these SPDEs into a more flexible framework, where less restrictions on the nonlinearities are needed, and we are able to treat rough initial values from critical spaces. Moreover, we will obtain higher-order regularity results." acknowledgement: "The authors thank Emiel Lorist for helpful comments. The authors thank the anonymous referees for their helpful remarks to improve the presentation.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria)." article_number: '56' 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: Mark full_name: Veraar, Mark last_name: Veraar citation: ama: Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in critical spaces part II. Journal of Evolution Equations. 2022;22(2). doi:10.1007/s00028-022-00786-7 apa: Agresti, A., & Veraar, M. (2022). Nonlinear parabolic stochastic evolution equations in critical spaces part II. Journal of Evolution Equations. Springer Nature. https://doi.org/10.1007/s00028-022-00786-7 chicago: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part II.” Journal of Evolution Equations. Springer Nature, 2022. https://doi.org/10.1007/s00028-022-00786-7. ieee: A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations in critical spaces part II,” Journal of Evolution Equations, vol. 22, no. 2. Springer Nature, 2022. ista: Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations in critical spaces part II. Journal of Evolution Equations. 22(2), 56. mla: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part II.” Journal of Evolution Equations, vol. 22, no. 2, 56, Springer Nature, 2022, doi:10.1007/s00028-022-00786-7. short: A. Agresti, M. Veraar, Journal of Evolution Equations 22 (2022). date_created: 2022-08-16T08:39:43Z date_published: 2022-06-01T00:00:00Z date_updated: 2023-08-03T12:53:51Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1007/s00028-022-00786-7 external_id: isi: - '000809108500001' file: - access_level: open_access checksum: 59b99d1b48b6bd40983e7ce298524a21 content_type: application/pdf creator: kschuh date_created: 2022-08-16T08:52:46Z date_updated: 2022-08-16T08:52:46Z file_id: '11862' file_name: 2022_Journal of Evolution Equations_Agresti.pdf file_size: 1758371 relation: main_file success: 1 file_date_updated: 2022-08-16T08:52:46Z has_accepted_license: '1' intvolume: ' 22' isi: 1 issue: '2' keyword: - Mathematics (miscellaneous) language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: Journal of Evolution Equations publication_identifier: eissn: - 1424-3202 issn: - 1424-3199 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Nonlinear parabolic stochastic evolution equations in critical spaces part II 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: 22 year: '2022' ... --- _id: '12145' abstract: - lang: eng text: In the class of strictly convex smooth boundaries each of which has no strip around its boundary foliated by invariant curves, we prove that the Taylor coefficients of the “normalized” Mather’s β-function are invariant under C∞-conjugacies. In contrast, we prove that any two elliptic billiard maps are C0-conjugate near their respective boundaries, and C∞-conjugate, near the boundary and away from a line passing through the center of the underlying ellipse. We also prove that, if the billiard maps corresponding to two ellipses are topologically conjugate, then the two ellipses are similar. acknowledgement: "We are grateful to the anonymous referees for their careful reading and valuable remarks and\r\ncomments which helped to improve the paper significantly. We gratefully acknowledge support from the European Research Council (ERC) through the Advanced Grant “SPERIG” (#885707)." article_processing_charge: No article_type: original author: - first_name: Edmond full_name: Koudjinan, Edmond id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E last_name: Koudjinan orcid: 0000-0003-2640-4049 - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 citation: ama: Koudjinan E, Kaloshin V. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 2022;27(6):525-537. doi:10.1134/S1560354722050021 apa: Koudjinan, E., & Kaloshin, V. (2022). On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. Springer Nature. https://doi.org/10.1134/S1560354722050021 chicago: Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” Regular and Chaotic Dynamics. Springer Nature, 2022. https://doi.org/10.1134/S1560354722050021. ieee: E. Koudjinan and V. Kaloshin, “On some invariants of Birkhoff billiards under conjugacy,” Regular and Chaotic Dynamics, vol. 27, no. 6. Springer Nature, pp. 525–537, 2022. ista: Koudjinan E, Kaloshin V. 2022. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 27(6), 525–537. mla: Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” Regular and Chaotic Dynamics, vol. 27, no. 6, Springer Nature, 2022, pp. 525–37, doi:10.1134/S1560354722050021. short: E. Koudjinan, V. Kaloshin, Regular and Chaotic Dynamics 27 (2022) 525–537. date_created: 2023-01-12T12:06:49Z date_published: 2022-10-03T00:00:00Z date_updated: 2023-08-04T08:59:14Z day: '03' department: - _id: VaKa doi: 10.1134/S1560354722050021 ec_funded: 1 external_id: arxiv: - '2105.14640' isi: - '000865267300002' intvolume: ' 27' isi: 1 issue: '6' keyword: - Mechanical Engineering - Applied Mathematics - Mathematical Physics - Modeling and Simulation - Statistical and Nonlinear Physics - Mathematics (miscellaneous) language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2105.14640 month: '10' oa: 1 oa_version: Preprint page: 525-537 project: - _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A call_identifier: H2020 grant_number: '885707' name: Spectral rigidity and integrability for billiards and geodesic flows publication: Regular and Chaotic Dynamics publication_identifier: eissn: - 1468-4845 issn: - 1560-3547 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - relation: erratum url: https://doi.org/10.1134/s1560354722060107 scopus_import: '1' status: public title: On some invariants of Birkhoff billiards under conjugacy type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 27 year: '2022' ... --- _id: '10549' abstract: - lang: eng text: We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on \mathbb {R}^d with stationary law (that is spatially homogeneous statistics) and fast decay of correlations on scales larger than the microscale \varepsilon >0, we establish homogenization error estimates of the order \varepsilon in case d\geqq 3, and of the order \varepsilon |\log \varepsilon |^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have been limited to a small algebraic rate of convergence \varepsilon ^\delta . We also establish error estimates for the approximation of the homogenized operator by the method of representative volumes of the order (L/\varepsilon )^{-d/2} for a representative volume of size L. Our results also hold in the case of systems for which a (small-scale) C^{1,\alpha } regularity theory is available. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 405009441. article_processing_charge: Yes (via OA deal) article_type: original author: - 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: Stefan full_name: Neukamm, Stefan last_name: Neukamm citation: ama: Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 2021;242(1):343-452. doi:10.1007/s00205-021-01686-9 apa: Fischer, J. L., & Neukamm, S. (2021). Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01686-9 chicago: Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01686-9. ieee: J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems,” Archive for Rational Mechanics and Analysis, vol. 242, no. 1. Springer Nature, pp. 343–452, 2021. ista: Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 242(1), 343–452. mla: Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive for Rational Mechanics and Analysis, vol. 242, no. 1, Springer Nature, 2021, pp. 343–452, doi:10.1007/s00205-021-01686-9. short: J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242 (2021) 343–452. date_created: 2021-12-16T12:12:33Z date_published: 2021-06-30T00:00:00Z date_updated: 2023-08-17T06:23:21Z day: '30' ddc: - '530' department: - _id: JuFi doi: 10.1007/s00205-021-01686-9 external_id: arxiv: - '1908.02273' isi: - '000668431200001' file: - access_level: open_access checksum: cc830b739aed83ca2e32c4e0ce266a4c content_type: application/pdf creator: cchlebak date_created: 2021-12-16T14:58:08Z date_updated: 2021-12-16T14:58:08Z file_id: '10558' file_name: 2021_ArchRatMechAnalysis_Fischer.pdf file_size: 1640121 relation: main_file success: 1 file_date_updated: 2021-12-16T14:58:08Z has_accepted_license: '1' intvolume: ' 242' isi: 1 issue: '1' keyword: - Mechanical Engineering - Mathematics (miscellaneous) - Analysis language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 343-452 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: Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems 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: 242 year: '2021' ... --- _id: '8418' abstract: - lang: eng text: For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set U in phase space of fixed measure, where the set of initial points which lead to collision is O(μ120) dense as μ→0. article_processing_charge: No article_type: original author: - first_name: Marcel full_name: Guardia, Marcel last_name: Guardia - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 - first_name: Jianlu full_name: Zhang, Jianlu last_name: Zhang citation: ama: Guardia M, Kaloshin V, Zhang J. Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and Analysis. 2019;233(2):799-836. doi:10.1007/s00205-019-01368-7 apa: Guardia, M., Kaloshin, V., & Zhang, J. (2019). Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-019-01368-7 chicago: Guardia, Marcel, Vadim Kaloshin, and Jianlu Zhang. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” Archive for Rational Mechanics and Analysis. Springer Nature, 2019. https://doi.org/10.1007/s00205-019-01368-7. ieee: M. Guardia, V. Kaloshin, and J. Zhang, “Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem,” Archive for Rational Mechanics and Analysis, vol. 233, no. 2. Springer Nature, pp. 799–836, 2019. ista: Guardia M, Kaloshin V, Zhang J. 2019. Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and Analysis. 233(2), 799–836. mla: Guardia, Marcel, et al. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” Archive for Rational Mechanics and Analysis, vol. 233, no. 2, Springer Nature, 2019, pp. 799–836, doi:10.1007/s00205-019-01368-7. short: M. Guardia, V. Kaloshin, J. Zhang, Archive for Rational Mechanics and Analysis 233 (2019) 799–836. date_created: 2020-09-17T10:41:51Z date_published: 2019-03-12T00:00:00Z date_updated: 2021-01-12T08:19:09Z day: '12' doi: 10.1007/s00205-019-01368-7 extern: '1' intvolume: ' 233' issue: '2' keyword: - Mechanical Engineering - Mathematics (miscellaneous) - Analysis language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1007/s00205-019-01368-7 month: '03' oa: 1 oa_version: Published Version page: 799-836 publication: Archive for Rational Mechanics and Analysis publication_identifier: issn: - 0003-9527 - 1432-0673 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 233 year: '2019' ... --- _id: '8508' abstract: - lang: eng text: We study generic unfoldings of homoclinic tangencies of two-dimensional area-preserving diffeomorphisms (conservative New house phenomena) and show that they give rise to invariant hyperbolic sets of arbitrarily large Hausdorff dimension. As applications, we discuss the size of the stochastic layer of a standard map and the Hausdorff dimension of invariant hyperbolic sets for certain restricted three-body problems. We avoid involved technical details and only concentrate on the ideas of the proof of the presented results. article_processing_charge: No article_type: original author: - first_name: Anton full_name: Gorodetski, Anton last_name: Gorodetski - first_name: Vadim full_name: Kaloshin, Vadim id: FE553552-CDE8-11E9-B324-C0EBE5697425 last_name: Kaloshin orcid: 0000-0002-6051-2628 citation: ama: Gorodetski A, Kaloshin V. Conservative homoclinic bifurcations and some applications. Proceedings of the Steklov Institute of Mathematics. 2009;267(1):76-90. doi:10.1134/s0081543809040063 apa: Gorodetski, A., & Kaloshin, V. (2009). Conservative homoclinic bifurcations and some applications. Proceedings of the Steklov Institute of Mathematics. Springer Nature. https://doi.org/10.1134/s0081543809040063 chicago: Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations and Some Applications.” Proceedings of the Steklov Institute of Mathematics. Springer Nature, 2009. https://doi.org/10.1134/s0081543809040063. ieee: A. Gorodetski and V. Kaloshin, “Conservative homoclinic bifurcations and some applications,” Proceedings of the Steklov Institute of Mathematics, vol. 267, no. 1. Springer Nature, pp. 76–90, 2009. ista: Gorodetski A, Kaloshin V. 2009. Conservative homoclinic bifurcations and some applications. Proceedings of the Steklov Institute of Mathematics. 267(1), 76–90. mla: Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations and Some Applications.” Proceedings of the Steklov Institute of Mathematics, vol. 267, no. 1, Springer Nature, 2009, pp. 76–90, doi:10.1134/s0081543809040063. short: A. Gorodetski, V. Kaloshin, Proceedings of the Steklov Institute of Mathematics 267 (2009) 76–90. date_created: 2020-09-18T10:48:03Z date_published: 2009-12-01T00:00:00Z date_updated: 2021-01-12T08:19:46Z day: '01' doi: 10.1134/s0081543809040063 extern: '1' intvolume: ' 267' issue: '1' keyword: - Mathematics (miscellaneous) language: - iso: eng month: '12' oa_version: None page: 76-90 publication: Proceedings of the Steklov Institute of Mathematics publication_identifier: issn: - 0081-5438 - 1531-8605 publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Conservative homoclinic bifurcations and some applications type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 267 year: '2009' ...