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On the global existence for the Muskat problem


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dc.creator Constantin, Peter es
dc.creator Córdoba Gazolaz, Diego es
dc.creator Gancedo García, Francisco es
dc.creator Strain, Robert M. es 2016-09-20T11:29:17Z 2016-09-20T11:29:17Z 2013
dc.identifier.citation Constantin, P., Córdoba Gazolaz, D., Gancedo García, F. y Strain, R.M. (2013). On the global existence for the Muskat problem. Journal of the European Mathematical Society, 15 (1), 201-227.
dc.identifier.issn 1435-9855 es
dc.identifier.issn 1435-9863 es
dc.description.abstract The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an $L^2(\R)$ maximum principle, in the form of a new ``log'' conservation law (???) which is satisfied by the equation (???) for the interface. Our second result is a proof of global existence of Lipschitz continuous solutions for initial data that satisfy ∥f0∥L∞<∞ and ∥∂xf0∥L∞<1. We take advantage of the fact that the bound ∥∂xf0∥L∞<1 is propagated by solutions, which grants strong compactness properties in comparison to the log conservation law. Lastly, we prove a global existence result for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance ∥f∥1≤1/5. Previous results of this sort used a small constant ϵ≪1 which was not explicit. es
dc.description.sponsorship National Science Foundation es
dc.description.sponsorship Ministerio de Ciencia e Innovación es
dc.description.sponsorship European Research Council es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher European Mathematical Society es
dc.relation.ispartof Journal of the European Mathematical Society, 15 (1), 201-227.
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri *
dc.subject Porous media es
dc.subject Incompressible flows es
dc.subject Fluid interface es
dc.subject Global existence es
dc.title On the global existence for the Muskat problem es
dc.type info:eu-repo/semantics/article es
dc.type.version info:eu-repo/semantics/submittedVersion es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Análisis Matemático es
dc.relation.projectID DMS-0804380 es
dc.relation.projectID MTM2008-03754 es
dc.relation.projectID StG-203138CDSIF es
dc.relation.projectID DMS-0901810 es
dc.relation.projectID DMS-0901463 es
dc.relation.publisherversion es
dc.identifier.doi 10.4171/JEMS/360 es Universidad de Sevilla. FQM104: Analisis Matematico es
idus.format.extent 31 p. es
dc.journaltitle Journal of the European Mathematical Society es
dc.publication.volumen 15 es
dc.publication.issue 1 es
dc.publication.initialPage 201 es
dc.publication.endPage 227 es
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