The primitive equations of the atmosphere in presence of vapor saturation

TL;DR

This paper develops a new mathematical formulation for the primitive equations of the atmosphere that incorporates vapor saturation and condensation effects, providing a comprehensive theory for solutions to this complex nonlinear system.

Contribution

It introduces a novel formulation using differential inclusions and variational inequalities to model phase transitions in atmospheric equations, establishing existence and uniqueness results.

Findings

Proved global existence of quasi-strong and strong solutions.

Established maximum principles relevant to physical phenomena.

Developed a new mathematical framework for coupled nonlinear PDEs with phase transitions.

Abstract

A modification of the classical primitive equations of the atmosphere is considered in order to take into account important phase transition phenomena due to air saturation and condensation. We provide a mathematical formulation of the problem that appears to be new in this setting, by making use of differential inclusions and variational inequalities, and which allows to develop a rather complete theory for the solutions to what turns out to be a nonlinearly coupled system of non-smooth partial differential equations. Specifically we prove global existence of quasi-strong and strong solutions, along with uniqueness results and maximum principles of physical interest.