dc.creator | Constantin, Peter | es |
dc.creator | Córdoba Gazolaz, Diego | es |
dc.creator | Gancedo García, Francisco | es |
dc.creator | Strain, Robert M. | es |
dc.date.accessioned | 2016-09-20T11:29:17Z | |
dc.date.available | 2016-09-20T11:29:17Z | |
dc.date.issued | 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.identifier.uri | http://hdl.handle.net/11441/45145 | |
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 | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
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 |
dcterms.identifier | https://ror.org/03yxnpp24 | |
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 | http://www.ems-ph.org/journals/show_pdf.php?issn=1435-9855&vol=15&iss=1&rank=7 | es |
dc.identifier.doi | 10.4171/JEMS/360 | es |
dc.contributor.group | 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 |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/45145 | |