Local solvability and turning for the inhomogeneous Muskat problem

In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane R 2 or a bounded strip S D R . =2; =2/. The system is in the stable regime if the denser fluid is be...

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Detalles Bibliográficos
Autores: Berselli, Luigi C., Córdoba, Diego, Granero Belinchón, Rafael|||0000-0003-2752-8086
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/30377
Acceso en línea:https://hdl.handle.net/10902/30377
Access Level:acceso abierto
Palabra clave:Darcy’s law
Inhomogeneous Muskat problem
Well-posedness
Blow-up
Maximum principle
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spelling Local solvability and turning for the inhomogeneous Muskat problemBerselli, Luigi C.Córdoba, DiegoGranero Belinchón, Rafael|||0000-0003-2752-8086Darcy’s lawInhomogeneous Muskat problemWell-posednessBlow-upMaximum principleIn this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane R 2 or a bounded strip S D R . =2; =2/. The system is in the stable regime if the denser fluid is below the lighter one. First, we show local existence in Sobolev spaces by means of energy method when the system is in the stable regime. Then we prove the existence of curves such that they start in the stable regime and in finite time they reach the unstable one. This change of regime (turning) was first proven in [5] for the homogenous Muskat problem with infinite depth.The authors are supported by the Grants MTM2011-26696 and SEV-2011- 0087 from Ministerio de Ciencia e Innovación (MICINN). Diego Córdoba was partially supported by StG-203138CDSIF of the ERC. Rafael Granero-Belinchón is grateful to the former Department of Applied Mathematics ”Ulisse Dini” of the Pisa University for the hospitality during May–July 2012. We are grateful tInstituto de Ciencias Matemáticas (Madrid) and to the Dipartimento di Ingegneria Aerospaziale (Pisa) for computing facilities.European Mathematical Society Publishing HouseUniversidad de Cantabria20142014-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/30377Interfaces and Free Boundaries, 2014, 16, 175-213reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/303772026-06-02T12:39:31Z
dc.title.none.fl_str_mv Local solvability and turning for the inhomogeneous Muskat problem
title Local solvability and turning for the inhomogeneous Muskat problem
spellingShingle Local solvability and turning for the inhomogeneous Muskat problem
Berselli, Luigi C.
Darcy’s law
Inhomogeneous Muskat problem
Well-posedness
Blow-up
Maximum principle
title_short Local solvability and turning for the inhomogeneous Muskat problem
title_full Local solvability and turning for the inhomogeneous Muskat problem
title_fullStr Local solvability and turning for the inhomogeneous Muskat problem
title_full_unstemmed Local solvability and turning for the inhomogeneous Muskat problem
title_sort Local solvability and turning for the inhomogeneous Muskat problem
dc.creator.none.fl_str_mv Berselli, Luigi C.
Córdoba, Diego
Granero Belinchón, Rafael|||0000-0003-2752-8086
author Berselli, Luigi C.
author_facet Berselli, Luigi C.
Córdoba, Diego
Granero Belinchón, Rafael|||0000-0003-2752-8086
author_role author
author2 Córdoba, Diego
Granero Belinchón, Rafael|||0000-0003-2752-8086
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Darcy’s law
Inhomogeneous Muskat problem
Well-posedness
Blow-up
Maximum principle
topic Darcy’s law
Inhomogeneous Muskat problem
Well-posedness
Blow-up
Maximum principle
description In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane R 2 or a bounded strip S D R . =2; =2/. The system is in the stable regime if the denser fluid is below the lighter one. First, we show local existence in Sobolev spaces by means of energy method when the system is in the stable regime. Then we prove the existence of curves such that they start in the stable regime and in finite time they reach the unstable one. This change of regime (turning) was first proven in [5] for the homogenous Muskat problem with infinite depth.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/30377
url https://hdl.handle.net/10902/30377
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv European Mathematical Society Publishing House
publisher.none.fl_str_mv European Mathematical Society Publishing House
dc.source.none.fl_str_mv Interfaces and Free Boundaries, 2014, 16, 175-213
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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