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

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

2011-02-09

arxiv.org/abs/1102.1902v2

Mathematics

Analysis of PDEs

38 pages, added new comments and a figure, corrected typos

Scientific paper

The Muskat problem models the evolution of the interface given by two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the 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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