The Lagrangian approach to the compressible primitive equations

TL;DR

This paper develops a hydrostatic Lagrangian framework for the compressible primitive equations, analyzing key operators and establishing well-posedness results for large and small data under different pressure laws.

Contribution

It introduces a novel hydrostatic Lagrangian approach and investigates the compressible hydrostatic Lamé and Stokes operators, providing new well-posedness results.

Findings

Established local strong well-posedness for large data.

Proved global strong well-posedness for small data.

Analyzed the effects of gravity and pressure laws on solutions.

Abstract

This article develops the hydrostatic Lagrangian approach to the compressible primitive equations. A fundamental aspect in the analysis is the investigation of the compressible hydrostatic Lam\'{e} and Stokes operators. Local strong well-posedness for large data and global strong well-posedness for small data are established under various assumptions on the pressure law, both in the presence and absence of gravity.