arXiv 1111.72022011-11math.AP

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

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

备注：: 16 pages, no figures

英文摘要：

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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