Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case

Alessio Figalli; Guido De Philippis; Luigi Ambrosio; Maria Colombo

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Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case

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arxiv 1111.7202 v4 pith:ZUHLCQ6P submitted 2011-11-30 math.AP

Luigi Ambrosio , Maria Colombo , Guido De Philippis , Alessio Figalli This is my paper

classification math.AP

keywords solutionsdimensionalequationsexistencesemigeostrophicalexandrovassumptionscase

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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.

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