Mixing solutions for the Muskat problem
  We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type $H^5$ initial data in the fully unstable regime. The proof combines convex integration, contour dynamics and a basic calculus for non smooth semiclassical type pseudodifferential operators which is developed. 
\'Angel Castro, Diego C\'ordoba and Daniel Faraco
math.AP