A global existence result for the semigeostrophic equations in three   dimensional convex domains
  Exploiting recent regularity estimates for the Monge-Amp\`ere equation, under some suitable assumptions on the initial data we prove global-in-time existence of Eulerian distributional solutions to the semigeostrophic equations in 3-dimensional convex domains. 
Luigi Ambrosio, Maria Colombo, Guido De Philippis, Alessio Figalli
math.AP