Inserted: 24 may 2012
Last Updated: 5 feb 2013
Journal: Discrete Contin. Dyn. Syst.
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