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

Pages 909-948 from Volume 175 (2012), Issue 2 by Ángel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, María López-Fernández

Abstract

The Muskat problem models the evolution of the interface between two different 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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Keywords
, , , , ,
DOI
https://doi.org/10.4007/annals.2012.175.2.9
MR
2993754
zbMATH
06025004
Milestones
Received: 8 February 2011
Revised: 30 May 2011
Accepted: 7 May 2011
Published online: 1 March 2012

Authors

Ángel Castro

Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain

Diego Córdoba

Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Cientíificas, 28049 Madrid, Spain

Charles Fefferman

Department of Mathematics, Princeton University, Fine Hall - Washington Rd., Princeton, NJ 08544

Francisco Gancedo

Department of Mathematical Analysis, University of Seville, C/ Tarfia s/n, Campus Reina Mercedes, 41012 Sevilla, Spain

María López-Fernández

Institut für Mathematik, Universität Zürich, Zürich, Switzerland