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

Tarek Zöchling

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arXiv · 2602.21348

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

Tarek Zöchling

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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.

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Tarek Zöchling. 2026-02-24. Global Strong Well-posedness of the heat-conducting, compressible primitive Equations. https://arxiv.org/abs/2602.21348

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