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Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves

Author
Castro, Ángel; Córdoba, Diego; Fefferman, Charles L.; Gancedo, Francisco; López-Fernández, María
Entity
UAM. Departamento de Matemáticas
Publisher
Princeton University, Department of Mathematics
Date
2012-03-01
Citation
Annals of Mathematics 175.2 (2012): 909-948
ISSN
0003-486X (print); 1939-8980 (online)
DOI
10.4007/annals.2012.175.2.9
Funded by
AC, DC and FG were partially supported by the grant MTM2008-03754 of the MCINN (Spain) and the grant StG-203138CDSIF of the ERC. CF was partially supported by NSF grant DMS-0901040 and ONR grant ONR00014-08-1-0678. FG was partially supported by NSF grant DMS-0901810. MLF was partially supported by the grants MTM2008-03541 and MTM2010-19510 of the MCINN (Spain).
Editor's Version
http://dx.doi.org/10.4007/annals.2012.175.2.9
Subjects
Breakdown; Darcy law; Incompressible flow; Interface dynamics; Rayleigh-Taylor; Water waves; Matemáticas
URI
http://hdl.handle.net/10486/662222
Note
The following article appeared in Annals of Mathematics 175.2 (2012): 909-948 and may be found at http://annals.math.princeton.edu/2012/175-2/p09
Rights
The Authors

Abstract

The Muskat problem models the evolution of the interface between two diff erent fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.
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Google™ Scholar:Castro, Ángel - Córdoba, Diego - Fefferman, Charles L. - Gancedo, Francisco - López-Fernández, María

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