Calculus of Variations and Geometric Measure Theory

L. Ambrosio - M. Colombo - G. De Philippis - A. Figalli

A global existence result for the semigeostrophic equations in three dimensional convex domains

created by colombom on 24 May 2012
modified by dephilipp on 30 Oct 2017


Accepted Paper

Inserted: 24 may 2012
Last Updated: 30 oct 2017

Journal: Discrete Contin. Dyn. Syst.
Year: 2012

ArXiv: 1205.5435 PDF


Exploiting recent regularity estimates for the Monge-Amp\`ere equation, under some suitable assumptions on the initial data we prove global-in-time existence of Eulerian distributional solutions to the semigeostrophic equations in 3-dimensional convex domains.

Keywords: optimal transportation, Semigeostrophic equations