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

Ángel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, María López-Fernández

Research output: Contribution to journalArticle

66 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)909-948
Number of pages40
JournalAnnals of Mathematics
Volume175
Issue number2
DOIs
StatePublished - Mar 1 2012

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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