Compressible primitive equations: Formal derivation and stability of weak solutions
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We present a formal derivation of compressible primitive equations for atmosphere modelling. They are obtained from the 3D compressible Navier- Stokes equations with an anisotropic viscous stress tensor depending on the density. Then, we study the stability of weak solutions to this problem by introducing an intermediate model obtained by a suitable change of variables. This intermediate model is more practical and it is simpler to achieve the main result.