[{"author":[{"full_name":"Marveggio, Alice","first_name":"Alice","last_name":"Marveggio","id":"25647992-AA84-11E9-9D75-8427E6697425"}],"related_material":{"record":[{"id":"11842","status":"public","relation":"part_of_dissertation"},{"id":"14597","status":"public","relation":"part_of_dissertation"}]},"date_created":"2023-11-21T11:41:05Z","date_updated":"2024-03-22T13:21:28Z","year":"2023","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).","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"JuFi"}],"publisher":"Institute of Science and Technology Austria","file_date_updated":"2024-03-20T12:28:32Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","doi":"10.15479/at:ista:14587","degree_awarded":"PhD","supervisor":[{"full_name":"Fischer, Julian L","first_name":"Julian L","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X"}],"language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)"},"project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","name":"Bridging Scales in Random Materials","call_identifier":"H2020"}],"month":"11","publication_identifier":{"issn":["2663 - 337X"]},"file":[{"date_updated":"2023-11-29T09:09:31Z","date_created":"2023-11-29T09:09:31Z","checksum":"6c7db4cc86da6cdc79f7f358dc7755d4","success":1,"relation":"main_file","file_id":"14626","content_type":"application/pdf","file_size":2881100,"creator":"amarvegg","file_name":"thesis_Marveggio.pdf","access_level":"open_access"},{"access_level":"closed","file_name":"Thesis_Marveggio.zip","creator":"amarvegg","content_type":"application/zip","file_size":10189696,"file_id":"14627","relation":"source_file","checksum":"52f28bdf95ec82cff39f3685f9c48e7d","date_created":"2023-11-29T09:10:19Z","date_updated":"2024-03-20T12:28:32Z"}],"oa_version":"Published Version","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"14587","title":"Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences","status":"public","ddc":["515"],"abstract":[{"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.","lang":"eng"}],"type":"dissertation","alternative_title":["ISTA Thesis"],"date_published":"2023-11-21T00:00:00Z","citation":{"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.","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.","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","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","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.","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."},"page":"228","day":"21","article_processing_charge":"No","has_accepted_license":"1"},{"oa_version":"Published Version","file":[{"file_id":"11848","relation":"main_file","date_created":"2022-08-16T06:55:22Z","date_updated":"2022-08-16T06:55:22Z","success":1,"checksum":"75c5f286300e6f0539cf57b4dba108d5","file_name":"2022_JMathFluidMech_Hensel.pdf","access_level":"open_access","creator":"cchlebak","file_size":2045570,"content_type":"application/pdf"}],"status":"public","ddc":["510"],"title":"Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities","intvolume":" 24","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"11842","abstract":[{"text":"We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier–Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With respect to the motion of the interface, we consider pure transport by the fluid flow. Along the boundary of the domain, a complete slip boundary condition for the fluid velocities and a constant ninety degree contact angle condition for the interface are assumed. In the present work, we devise for the resulting evolution problem a suitable weak solution concept based on the framework of varifolds and establish as the main result a weak-strong uniqueness principle in 2D. The proof is based on a relative entropy argument and requires a non-trivial further development of ideas from the recent work of Fischer and the first author (Arch. Ration. Mech. Anal. 236, 2020) to incorporate the contact angle condition. To focus on the effects of the necessarily singular geometry of the evolving fluid domains, we work for simplicity in the regime of same viscosities for the two fluids.","lang":"eng"}],"issue":"3","type":"journal_article","date_published":"2022-08-01T00:00:00Z","article_type":"original","publication":"Journal of Mathematical Fluid Mechanics","citation":{"ama":"Hensel S, Marveggio A. Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. 2022;24(3). doi:10.1007/s00021-022-00722-2","ista":"Hensel S, Marveggio A. 2022. Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. 24(3), 93.","apa":"Hensel, S., & Marveggio, A. (2022). Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. Springer Nature. https://doi.org/10.1007/s00021-022-00722-2","ieee":"S. Hensel and A. Marveggio, “Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities,” Journal of Mathematical Fluid Mechanics, vol. 24, no. 3. Springer Nature, 2022.","mla":"Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.” Journal of Mathematical Fluid Mechanics, vol. 24, no. 3, 93, Springer Nature, 2022, doi:10.1007/s00021-022-00722-2.","short":"S. Hensel, A. Marveggio, Journal of Mathematical Fluid Mechanics 24 (2022).","chicago":"Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.” Journal of Mathematical Fluid Mechanics. Springer Nature, 2022. https://doi.org/10.1007/s00021-022-00722-2."},"day":"01","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","date_updated":"2024-03-22T13:21:27Z","date_created":"2022-08-14T22:01:45Z","volume":24,"author":[{"full_name":"Hensel, Sebastian","first_name":"Sebastian","last_name":"Hensel","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-7252-8072"},{"full_name":"Marveggio, Alice","last_name":"Marveggio","first_name":"Alice","id":"25647992-AA84-11E9-9D75-8427E6697425"}],"related_material":{"record":[{"id":"14587","status":"public","relation":"dissertation_contains"}]},"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"JuFi"}],"acknowledgement":"The authors warmly thank their former resp. current PhD advisor Julian Fischer for the suggestion of this problem and for valuable initial discussions on the subjects of this paper. 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.","year":"2022","license":"https://creativecommons.org/licenses/by/4.0/","file_date_updated":"2022-08-16T06:55:22Z","ec_funded":1,"article_number":"93","language":[{"iso":"eng"}],"doi":"10.1007/s00021-022-00722-2","isi":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2112.11154"],"isi":["000834834300001"]},"oa":1,"month":"08","publication_identifier":{"issn":["1422-6928"],"eissn":["1422-6952"]}},{"type":"preprint","abstract":[{"text":"Phase-field models such as the Allen-Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen-Cahn equation with a potential with N≥3 distinct minima has been conjectured to describe the evolution of branched interfaces by multiphase mean curvature flow.\r\nIn the present work, we give a rigorous proof for this statement in two and three ambient dimensions and for a suitable class of potentials: As long as a strong solution to multiphase mean curvature flow exists, solutions to the vectorial Allen-Cahn equation with well-prepared initial data converge towards multiphase mean curvature flow in the limit of vanishing interface width parameter ε↘0. We even establish the rate of convergence O(ε1/2).\r\nOur approach is based on the gradient flow structure of the Allen-Cahn equation and its limiting motion: Building on the recent concept of \"gradient flow calibrations\" for multiphase mean curvature flow, we introduce a notion of relative entropy for the vectorial Allen-Cahn equation with multi-well potential. This enables us to overcome the limitations of other approaches, e.g. avoiding the need for a stability analysis of the Allen-Cahn operator or additional convergence hypotheses for the energy at positive times.","lang":"eng"}],"ec_funded":1,"status":"public","title":"Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow","publication_status":"submitted","department":[{"_id":"JuFi"}],"year":"2022","_id":"14597","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_created":"2023-11-23T09:30:02Z","date_updated":"2024-03-22T13:21:27Z","oa_version":"Preprint","author":[{"last_name":"Fischer","first_name":"Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","full_name":"Fischer, Julian L"},{"id":"25647992-AA84-11E9-9D75-8427E6697425","last_name":"Marveggio","first_name":"Alice","full_name":"Marveggio, Alice"}],"related_material":{"record":[{"id":"14587","status":"public","relation":"dissertation_contains"}]},"month":"03","day":"31","article_processing_charge":"No","project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819"}],"publication":"arXiv","external_id":{"arxiv":["2203.17143"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2203.17143"}],"citation":{"chicago":"Fischer, Julian L, and Alice Marveggio. “Quantitative Convergence of the Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2203.17143.","short":"J.L. Fischer, A. Marveggio, ArXiv (n.d.).","mla":"Fischer, Julian L., and Alice Marveggio. “Quantitative Convergence of the Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, doi:10.48550/ARXIV.2203.17143.","ieee":"J. L. Fischer and A. Marveggio, “Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow,” arXiv. .","apa":"Fischer, J. L., & Marveggio, A. (n.d.). Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv. https://doi.org/10.48550/ARXIV.2203.17143","ista":"Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv, 10.48550/ARXIV.2203.17143.","ama":"Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv. doi:10.48550/ARXIV.2203.17143"},"language":[{"iso":"eng"}],"date_published":"2022-03-31T00:00:00Z","doi":"10.48550/ARXIV.2203.17143"},{"publication":"Journal of Differential Equations","citation":{"mla":"Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard Model Based on a Microforce Balance.” Journal of Differential Equations, vol. 274, no. 2, Elsevier, 2021, pp. 924–70, doi:10.1016/j.jde.2020.10.030.","short":"A. Marveggio, G. Schimperna, Journal of Differential Equations 274 (2021) 924–970.","chicago":"Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard Model Based on a Microforce Balance.” Journal of Differential Equations. Elsevier, 2021. https://doi.org/10.1016/j.jde.2020.10.030.","ama":"Marveggio A, Schimperna G. On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. 2021;274(2):924-970. doi:10.1016/j.jde.2020.10.030","ista":"Marveggio A, Schimperna G. 2021. On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. 274(2), 924–970.","apa":"Marveggio, A., & Schimperna, G. (2021). On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2020.10.030","ieee":"A. Marveggio and G. Schimperna, “On a non-isothermal Cahn-Hilliard model based on a microforce balance,” Journal of Differential Equations, vol. 274, no. 2. Elsevier, pp. 924–970, 2021."},"article_type":"original","page":"924-970","date_published":"2021-02-15T00:00:00Z","scopus_import":"1","day":"15","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"8792","status":"public","title":"On a non-isothermal Cahn-Hilliard model based on a microforce balance","intvolume":" 274","oa_version":"Preprint","type":"journal_article","abstract":[{"text":"This paper is concerned with a non-isothermal Cahn-Hilliard model based on a microforce balance. The model was derived by A. Miranville and G. Schimperna starting from the two fundamental laws of Thermodynamics, following M. Gurtin's two-scale approach. The main working assumptions are made on the behaviour of the heat flux as the absolute temperature tends to zero and to infinity. A suitable Ginzburg-Landau free energy is considered. Global-in-time existence for the initial-boundary value problem associated to the entropy formulation and, in a subcase, also to the weak formulation of the model is proved by deriving suitable a priori estimates and by showing weak sequential stability of families of approximating solutions. At last, some highlights are given regarding a possible approximation scheme compatible with the a-priori estimates available for the system.","lang":"eng"}],"issue":"2","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2004.02618","open_access":"1"}],"external_id":{"isi":["000600845300023"],"arxiv":["2004.02618"]},"isi":1,"quality_controlled":"1","doi":"10.1016/j.jde.2020.10.030","language":[{"iso":"eng"}],"month":"02","publication_identifier":{"issn":["00220396"],"eissn":["10902732"]},"year":"2021","acknowledgement":"G. Schimperna has been partially supported by GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica).","publication_status":"published","department":[{"_id":"JuFi"}],"publisher":"Elsevier","author":[{"full_name":"Marveggio, Alice","first_name":"Alice","last_name":"Marveggio","id":"25647992-AA84-11E9-9D75-8427E6697425"},{"first_name":"Giulio","last_name":"Schimperna","full_name":"Schimperna, Giulio"}],"date_created":"2020-11-22T23:01:26Z","date_updated":"2023-08-04T11:12:16Z","volume":274}]