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

Type: Article

Publication Date: 2012-01-01

Citations: 52

DOI: https://doi.org/10.1080/03605302.2012.669443

Abstract

In this article we use new regularity and stability estimates for Alexandrov solutions to Monge-Ampère equations, recently established by De Philippis and Figalli [14 De Philippis , G. , Figalli , A. W2, 1 regularity for solutions of the Monge-Ampère equation. Preprint. [Google Scholar]], 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.

Locations

Communications in Partial Differential Equations - View
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