On the existence and weak stability of solutions to the compressible semigeostrophic equations

In this article, existence and weak stability of solutions to the compressible semigeostrophic equations are studied both in physical and in dual spaces. We present a proof of the existence of a weak solution to these equations in dual space assuming initial data in L 1 ( R 3 ) , extending previous results (Cullen and Maroofi (2003) [8]). An extension to the concept of Lagrangian solutions due to Cullen and Feldman (2006) [6] is presented to the compressible semigeostrophic system, and it is shown the existence of Lagrangian solutions in physical space, with initial potential vorticities in L 1 , as well a weak stability result with respect to perturbations of the potential vorticity in L 1 .