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arXiv · 2605.11754

Global Existence and Uniqueness of Strong Solutions for a Phase Transition Model in Atmospheric Dynamics

Giada Cianfarani Carnevale·Donatella Donatelli·Stefano Spirito
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Abstract

In this work, we study a phase transition model in atmospheric dynamics, inspired by the works [6,14,15], which analyze the primitive equations governing the evolution of velocity, temperature, and specific humidity. The main difficulty arises from the presence of a multivalued discontinuous nonlinear term in the temperature and in the humidity equations, describing the formation of precipitations, which becomes active under supersaturation conditions. To overcome this issue, we introduce a regularized formulation that ensures the existence and uniqueness of approximate solutions. By employing classical compactness arguments, we then establish the existence of a strong solution to the original model. Additionally, we establish uniqueness under a conditional and physically meaningful assumption. This approach allows us to provide a rigorous justification of the tropical climate model on the whole space $\mathbb{R}^2$, while avoiding the introduction of a viscosity term in the humidity equation.

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Giada Cianfarani Carnevale, Donatella Donatelli, Stefano Spirito. 2026-05-12. Global Existence and Uniqueness of Strong Solutions for a Phase Transition Model in Atmospheric Dynamics. https://arxiv.org/abs/2605.11754

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