Existence of a global weak solution to Compressible Primitive Equations

In this Note, we show a global weak existence result for a two dimensional Compressible Primitive Equations for atmosphere dynamics modeling

Compressible primitive equation: formal derivation and stability of weak solutions

We present a formal derivation of a simplified version of Compressible Primitive Equations (CPEs) for atmosphere modeling. They are obtained from $3$-D compressible Navier-Stokes equations with an \emph{anisotropic viscous stress tensor} where viscosity depends on the density. We then study the stability of the weak solutions of this model by using an intermediate model, called model problem, which is more simple and practical, to achieve the main result