Rayleigh-Taylor breakdown for the Muskat problem with applications to   water waves
  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. 
Angel Castro, Diego Cordoba, Charles Fefferman, Francisco Gancedo and   Maria Lopez-Fernandez
math.AP