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

 

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Author: Castro Martínez, Ángel
Córdoba Gazolaz, Diego
Fefferman, Charles L.
Gancedo García, Francisco
López Fernández, María
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2012
Published in: Annals of Mathematics, 175, 909-948.
Document type: Article
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.
Cite: Castro Martínez, Á., Córdoba Gazolaz, D., Fefferman, C.L., Gancedo García, F. y López Fernández, M. (2012). Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves. Annals of Mathematics, 175, 909-948.
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URI: http://hdl.handle.net/11441/45341

DOI: 10.4007/annals.2012.175.2.9

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