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Well-posedness of the Muskat problem with H2 initial data

dc.contributor.authorCheng, Arthur C. H.
dc.contributor.authorGranero Belinchón, Rafael 
dc.contributor.authorShkoller, Steve
dc.contributor.otherUniversidad de Cantabriaes_ES
dc.date.accessioned2023-08-03T10:13:18Z
dc.date.available2023-08-03T10:13:18Z
dc.date.issued2016
dc.identifier.issn0001-8708
dc.identifier.issn1090-2082
dc.identifier.urihttps://hdl.handle.net/10902/29595
dc.description.abstractWe study the dynamics of the interface between two incompressible fluids in a two-dimensional porous medium whose flow is modeled by the Muskat equations. For the two-phase Muskat problem, we establish global well-posedness and decay to equilibrium for small H2 perturbations of the rest state. For the one-phase Muskat problem, we prove local well-posedness for H2 initial data of arbitrary size. Finally, we show that solutions to the Muskat equations instantaneously become infinitely smooth.es_ES
dc.description.sponsorshipAC was supported by the Ministry of Science and Technology (Taiwan) under grant MOST-103- 2115-M-008-010-MY2 and by the National Center of Theoretical Sciences. RGB was supported by OxPDE via the EPSRC grant EP/I01893X/1. SS was supported by the National Science Foundation under grant and DMS-1301380, by OxPDE at the University of Oxford, and by the Royal Society WolfsonMerit Award. Some of this work was completed during the programFree Boundary Problems and Related Topics at the Isaac Newton Institute for Mathematical Sciences at Cambridge, UK. We are grateful to the organizers, Gui-Qiang Chen, Henrik Shahgholian and Juan Luis Vázquez, for both the invitation to participate in the program and to contribute to this special volume.es_ES
dc.format.extent49 p.es_ES
dc.language.isoenges_ES
dc.publisherElsevieres_ES
dc.rights©2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 licensees_ES
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.sourceAdvances in Mathematics 2016, 286, 32-104es_ES
dc.titleWell-posedness of the Muskat problem with H2 initial dataes_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.relation.publisherVersionhttps://doi.org/10.1016/j.aim.2015.08.026es_ES
dc.rights.accessRightsopenAccesses_ES
dc.identifier.DOI10.1016/j.aim.2015.08.026
dc.type.versionacceptedVersiones_ES


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