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

Abstract

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.

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