Finite time singularities for the free boundary incompressible Euler   equations
  In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem), for which the smoothness of the interface breaks down in finite time into a splash singularity or a splat singularity. 
Angel Castro, Diego C\'ordoba, Charles Fefferman, Francisco Gancedo   and Javier G\'omez-Serrano
math.AP math-ph math.MP physics.flu-dyn