Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: the 2-dimensional Periodic Case
نویسندگان
چکیده
In this paper we use new regularity and stability estimates for Alexandrov solutions to Monge-Ampère equations, recently estabilished by De Philippis and Figalli [14], 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.
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