Calculus of Variations and Geometric Measure Theory

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 dephilipp on 30 Oct 2017


Accepted Paper

Inserted: 30 nov 2011
Last Updated: 30 oct 2017

Journal: Comm. Partial Differential Equations
Year: 2012

ArXiv: 1111.7202 PDF


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.

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