Inserted: 24 may 2012
Last Updated: 30 oct 2017
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