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

Ángel Castro Vázquez, Diego Córdoba Gazolaz, Charles L. Fefferman, Francisco Gancedo García, María López Fernández

• 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.