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

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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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