Global Existence and Uniqueness of Strong Solutions for a Phase Transition Model in Atmospheric Dynamics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909035407605760 |
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| author | Carnevale, Giada Cianfarani Donatelli, Donatella Spirito, Stefano |
| author_facet | Carnevale, Giada Cianfarani Donatelli, Donatella Spirito, Stefano |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11754 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Existence and Uniqueness of Strong Solutions for a Phase Transition Model in Atmospheric Dynamics Carnevale, Giada Cianfarani Donatelli, Donatella Spirito, Stefano Analysis of PDEs 35D35, 76D03, 86A10, 35Q35, 76U05, 80A22 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. |
| title | Global Existence and Uniqueness of Strong Solutions for a Phase Transition Model in Atmospheric Dynamics |
| topic | Analysis of PDEs 35D35, 76D03, 86A10, 35Q35, 76U05, 80A22 |
| url | https://arxiv.org/abs/2605.11754 |