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

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

2011-11-30

arxiv.org/abs/1111.7202v2

Mathematics

Analysis of PDEs

16 pages, no figures

Scientific paper

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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