On the existence of stationary splash singularities for the Euler   equations
  In this paper we discuss the existence of stationary incompressible fluids with splash singularities. Specifically, we show that there are stationary solutions to the Euler equations with two fluids whose interfaces are arbitrarily close to a splash, and that there are stationary water waves with splash singularities. 
Diego C\'ordoba, Alberto Enciso and Nastasia Grubic
math.AP