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.
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
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