Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case
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.
The paper is available on the
cvgmt preprint server.