Global Strong Well-posedness of the heat-conducting, compressible primitive Equations

TL;DR

This paper proves the global strong well-posedness of heat-conducting, compressible primitive equations with temperature effects, extending previous results beyond the isothermal case using novel mathematical techniques.

Contribution

It introduces a new approach combining a structural density representation and a Lagrangian transformation to establish well-posedness for these complex equations.

Findings

Global strong solutions exist for small perturbations.

The results extend to non-isothermal regimes.

A new mathematical framework is developed for analysis.

Abstract

The full heat-conducting compressible primitive equations are considered, extending the compressible primitive-equation framework by coupling the temperature through the ideal gas law and the thermal energy balance in the presence of gravity. Global strong well-posedness is established for small perturbations of an equilibrium state, thereby providing a result beyond the isothermal regime. The proof relies on a structural representation of the density in terms of the temperature and on a new Lagrangian transformation.