Abstract
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 L1(R3), 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 L1, as well a weak stability result with respect to perturbations of the potential vorticity in L1.
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