  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.
