Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - M. Colombo - G. De Philippis - A. Figalli

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

created by ambrosio on 30 Nov 2011
modified by colombom on 14 Nov 2012


Accepted Paper

Inserted: 30 nov 2011
Last Updated: 14 nov 2012

Journal: Comm. Partial Differential Equations
Year: 2012


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 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.

Tags: GeMeThNES
Keywords: optimal transportation, Lagrangian flow, Semigeostrophic equations


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