Existence of a weak solution for the semigeostrophic equation with integrable initial data

Abstract

In this article we present a proof of existence of a weak solution for the semigeostrophic system of equations, formulated as an active scalar transport equation with Monge-Ampere coupling, with initial data in L-c(1) (R-3). This is an extension of a 1998 result due to Benamou and Brenier, who proved existence with initial data in L-c(p)(R-3), p > 3.o TEXTO COMPLETO DESTE ARTIGO, ESTARÁ DISPONÍVEL À PARTIR DE AGOSTO DE 2015.132232933