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Porous media: The
{M}uskat problem in three dimensions
Antonio Córdoba, Diego Córdoba and Francisco Gancedo |
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Vol. 6 (2013), No. 2, 447–497
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Abstract |
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The Muskat problem involves filtration of two incompressible fluids through a porous medium. We consider the problem in three dimensions, discussing the relevance of the Rayleigh–Taylor condition and the topology of the initial interface, in order to prove the local existence of solutions in Sobolev spaces. |
Keywords
porous media, incompressible flow, free boundary, Muskat
problem, local existence
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Mathematical Subject Classification 2010
Primary: 35Q35, 76S05, 76D05
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Milestones
Received: 1 December 2011
Accepted: 23 May 2012
Published: 24 June 2013
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Authors |
| Antonio Córdoba | |
| Instituto de Ciencias
Matemáticas-CSIC-UAM-UC3M-UCM and Departamento de
Matemáticas Universidad Autónoma de Madrid 28049 Madrid Spain |
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| Diego Córdoba | |
| Instituto de Ciencias
Matemáticas Consejo Superior de Investigaciones Científicas 28006 Madrid Spain |
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| Francisco Gancedo | |
| Department of Mathematics University of Chicago Chicago, IL 60637 United States |
Departamento de Análisis
Matemático Universidad de Sevilla 41012 Sevilla Spain |
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