Inserted: 30 nov 2011
Last Updated: 14 nov 2012
Journal: Comm. Partial Differential Equations
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 global in time existence of distributional solutions to the semigeostrophic equations on the 2-dimensional torus, under very mild assumptions on the initial data. A link with Lagrangian solutions is also discussed.
Keywords: optimal transportation, Lagrangian flow, Semigeostrophic equations