Some recent results on the Muskat problem

Angel Castro[1]; Diego Córdoba[1]; Francisco Gancedo[2]

  • [1] Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain
  • [2] Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637

Journées Équations aux dérivées partielles (2010)

  • Volume: 299, Issue: 2, page 1-14
  • ISSN: 0752-0360

Abstract

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We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the two-phase Hele-Shaw cell. The purpose of this paper is to outline recent results on local existence, weak solutions, maximum principles and global existence.

How to cite

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Castro, Angel, Córdoba, Diego, and Gancedo, Francisco. "Some recent results on the Muskat problem." Journées Équations aux dérivées partielles 299.2 (2010): 1-14. <http://eudml.org/doc/116386>.

@article{Castro2010,
abstract = {We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the two-phase Hele-Shaw cell. The purpose of this paper is to outline recent results on local existence, weak solutions, maximum principles and global existence.},
affiliation = {Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain; Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain; Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637},
author = {Castro, Angel, Córdoba, Diego, Gancedo, Francisco},
journal = {Journées Équations aux dérivées partielles},
keywords = {multiple fluids; porous media; Hele-Shaw problems},
language = {eng},
month = {6},
number = {2},
pages = {1-14},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Some recent results on the Muskat problem},
url = {http://eudml.org/doc/116386},
volume = {299},
year = {2010},
}

TY - JOUR
AU - Castro, Angel
AU - Córdoba, Diego
AU - Gancedo, Francisco
TI - Some recent results on the Muskat problem
JO - Journées Équations aux dérivées partielles
DA - 2010/6//
PB - Groupement de recherche 2434 du CNRS
VL - 299
IS - 2
SP - 1
EP - 14
AB - We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the two-phase Hele-Shaw cell. The purpose of this paper is to outline recent results on local existence, weak solutions, maximum principles and global existence.
LA - eng
KW - multiple fluids; porous media; Hele-Shaw problems
UR - http://eudml.org/doc/116386
ER -

References

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