Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
EntityUAM. Departamento de Matemáticas
PublisherPrinceton University, Department of Mathematics
10.4007/annals.2012.175.2.9Annals of Mathematics 175.2 (2012): 909-948
ISSN0003-486X (print); 1939-8980 (online)
Funded byAC, 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).
SubjectsBreakdown; Darcy law; Incompressible flow; Interface dynamics; Rayleigh-Taylor; Water waves; Matemáticas
NoteThe 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
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.
Google Scholar:Castro, Ángel - Córdoba, Diego - Fefferman, Charles L. - Gancedo, Francisco - López-Fernández, María
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Córdoba, Antonio; Córdoba, Diego; Gancedo, Francisco