Existence of Eulerian solutions to the semigeostrophic equations in   physical space: the 2-dimensional periodic case
  In this paper we use the new regularity and stability estimates for Alexandrov solutions to Monge-Ampere equations estabilished by G.De Philippis and A.Figalli to provide a global in time existence of distributional solutions to a semigeostrophic equation on the 2-dimensional torus, under very mild assumptions on the initial data. A link with Lagrangian solutions is also discussed. 
Luigi Ambrosio, Maria Colombo, Guido De Philippis, Alessio Figalli
math.AP