Vol. 6, No. 2, 2013

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Porous media: The {M}uskat problem in three dimensions

Antonio Córdoba, Diego Córdoba and Francisco Gancedo

Vol. 6 (2013), No. 2, 447–497

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.

porous media, incompressible flow, free boundary, Muskat problem, local existence
Mathematical Subject Classification 2010
Primary: 35Q35, 76S05, 76D05
Received: 1 December 2011
Accepted: 23 May 2012
Published: 24 June 2013
Antonio Córdoba
Instituto de Ciencias Matemáticas-CSIC-UAM-UC3M-UCM and Departamento de Matemáticas
Universidad Autónoma de Madrid
28049 Madrid
Diego Córdoba
Instituto de Ciencias Matemáticas
Consejo Superior de Investigaciones Científicas
28006 Madrid
Francisco Gancedo
Department of Mathematics
University of Chicago
Chicago, IL 60637
United States
Departamento de Análisis Matemático
Universidad de Sevilla
41012 Sevilla