Existence and weak–strong uniqueness for Maxwell–Stefan–Cahn–Hilliard systems

dc.contributor.authorHuo, Xiaokai
dc.contributor.authorJüngel, Ansgar
dc.contributor.authorTzavaras, Athanasios
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.institutionTechnische Universität Wien, Austria
dc.date.accessioned2023-06-13T11:46:13Z
dc.date.available2022-05-16T07:03:50Z
dc.date.available2023-02-26T06:13:11Z
dc.date.available2023-06-13T11:46:13Z
dc.date.issued2023-06-07
dc.description.abstractA Maxwell--Stefan system for fluid mixtures with driving forces depending on Cahn–Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a bounded domain with no-flux boundary conditions. The nonconvex part of the energy is assumed to have a bounded Hessian. The main difficulty of the analysis is the degeneracy of the diffusion matrix, which is overcome by proving the positive-definiteness of the matrix on a subspace and using the Bott–Duffin matrix inverse. The global existence of weak solutions and a weak–strong uniqueness property are shown by a careful combination of (relative) energy and entropy estimates, yielding H2(Ω) bounds for the densities, which cannot be obtained from the energy or entropy inequalities alone.
dc.description.sponsorshipXH and AJ acknowledge partial support from the Austrian Science Fund (FWF), grants P33010, W1245, and F65. AET acknowledges support from baseline funds of the King Abdullah University of Science and Technology (KAUST). This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, ERC Advance grant number 101018153.
dc.eprint.versionPost-print
dc.identifier.arxivid2205.06478
dc.identifier.citationHuo, X., Jüngel, A., & Tzavaras, A. E. (2023). Existence and weak–strong uniqueness for Maxwell–Stefan–Cahn–Hilliard systems. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire. https://doi.org/10.4171/aihpc/89
dc.identifier.doi10.4171/aihpc/89
dc.identifier.issn0294-1449
dc.identifier.issn1873-1430
dc.identifier.journalAnnales de l'Institut Henri Poincaré C, Analyse non linéaire
dc.identifier.urihttp://hdl.handle.net/10754/677939
dc.publisherEuropean Mathematical Society - EMS - Publishing House GmbH
dc.relation.urlhttps://ems.press/doi/10.4171/aihpc/89
dc.rightsArchived with thanks to Annales de l'Institut Henri Poincaré C, Analyse non linéaire under a Creative Commons license, details at: https://creativecommons.org/licenses/by/4.0/
dc.titleExistence and weak–strong uniqueness for Maxwell–Stefan–Cahn–Hilliard systems
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Huo, Xiaokai,equals">Huo, Xiaokai</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Jüngel, Ansgar,equals">Jüngel, Ansgar</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0002-1896-2270&spc.sf=dc.date.issued&spc.sd=DESC">Tzavaras, Athanasios</a> <a href="https://orcid.org/0000-0002-1896-2270" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Applied Mathematics and Computational Science Program,equals">Applied Mathematics and Computational Science Program</a><br><br><h5>Date</h5>2023-06-07</span>
display.details.right<span><h5>Abstract</h5>A Maxwell--Stefan system for fluid mixtures with driving forces depending on Cahn–Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a bounded domain with no-flux boundary conditions. The nonconvex part of the energy is assumed to have a bounded Hessian. The main difficulty of the analysis is the degeneracy of the diffusion matrix, which is overcome by proving the positive-definiteness of the matrix on a subspace and using the Bott–Duffin matrix inverse. The global existence of weak solutions and a weak–strong uniqueness property are shown by a careful combination of (relative) energy and entropy estimates, yielding H2(Ω) bounds for the densities, which cannot be obtained from the energy or entropy inequalities alone.<br><br><h5>Citation</h5>Huo, X., Jüngel, A., & Tzavaras, A. E. (2023). Existence and weak–strong uniqueness for Maxwell–Stefan–Cahn–Hilliard systems. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire. https://doi.org/10.4171/aihpc/89<br><br><h5>Acknowledgements</h5>XH and AJ acknowledge partial support from the Austrian Science Fund (FWF), grants P33010, W1245, and F65. AET acknowledges support from baseline funds of the King Abdullah University of Science and Technology (KAUST). This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, ERC Advance grant number 101018153.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=European Mathematical Society - EMS - Publishing House GmbH,equals">European Mathematical Society - EMS - Publishing House GmbH</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Annales de l'Institut Henri Poincaré C, Analyse non linéaire,equals">Annales de l'Institut Henri Poincaré C, Analyse non linéaire</a><br><br><h5>DOI</h5><a href="https://doi.org/10.4171/aihpc/89">10.4171/aihpc/89</a><br><br><h5>arXiv</h5><a href="https://arxiv.org/abs/2205.06478">2205.06478</a><br><br><h5>Additional Links</h5>https://ems.press/doi/10.4171/aihpc/89</span>
kaust.acknowledged.supportUnitBaseline funds
kaust.personTzavaras, Athanasios
orcid.authorHuo, Xiaokai
orcid.authorJüngel, Ansgar
orcid.authorTzavaras, Athanasios::0000-0002-1896-2270
orcid.id0000-0002-1896-2270
pubs.publication-statusPublished
refterms.dateFOA2022-05-16T07:05:12Z
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