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.
@incollection{JEDP_2010____A5_0,
author = {Castro, Angel and C\'ordoba, Diego and Gancedo, Francisco},
title = {Some recent results on the {Muskat} problem},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {5},
pages = {1--14},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2010},
doi = {10.5802/jedp.62},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.62/}
}
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 PY - 2010 SP - 1 EP - 14 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.62/ DO - 10.5802/jedp.62 LA - en ID - JEDP_2010____A5_0 ER -
%0 Journal Article %A Castro, Angel %A Córdoba, Diego %A Gancedo, Francisco %T Some recent results on the Muskat problem %J Journées équations aux dérivées partielles %D 2010 %P 1-14 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.62/ %R 10.5802/jedp.62 %G en %F JEDP_2010____A5_0
Castro, Angel; Córdoba, Diego; Gancedo, Francisco. Some recent results on the Muskat problem. Journées équations aux dérivées partielles (2010), article no. 5, 14 p. doi : 10.5802/jedp.62. http://www.numdam.org/articles/10.5802/jedp.62/
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