Structural stability for the splash singularities of the water waves   problem
  In this paper we show a structural stability result for water waves. The main motivation for this result is that we would like to exhibit a water wave whose interface starts as a graph and ends in a splash. Numerical simulations lead to an approximate solution with the desired behaviour. The stability result will conclude that near the approximate solution to water waves there is an exact solution. 
Angel Castro, Diego C\'ordoba, Charles Fefferman, Francisco Gancedo,   Javier G\'omez-Serrano
math.AP