Non-splat singularity for the one-phase Muskat problem
  For the water waves equations, the existence of splat singularities has been shown in [3], i.e., the interface self-intersects along an arc in finite time. The aim of this paper is to show the absence of splat singularities for the incompressible fluid dynamics in porous media. 
Diego C\'ordoba and Tania Pernas-Casta\~no
math.AP