Compressible primitive equation: formal derivation and stability of weak solutions

TL;DR

This paper derives a simplified compressible primitive equations model from 3D Navier-Stokes equations with density-dependent viscosity and analyzes the stability of its weak solutions using an intermediate model.

Contribution

It provides a formal derivation of a simplified atmospheric model from fundamental equations and establishes stability results for weak solutions.

Findings

Derived a simplified CPE model from 3D Navier-Stokes equations.

Proved stability of weak solutions using an intermediate model.

Enhanced understanding of atmospheric modeling stability.

Abstract

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.