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arXiv · 2507.07546

The primitive equations for the ocean and atmosphere in anisotropic spaces

Valentin Lemarié
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Abstract

In this work, we study the well-posedness of the primitive equations for the ocean and the atmosphere on two specific domains: a bounded domain $\Omega_1\mathrel{\mathop:}=(-1,1)^3$ with periodic boundary conditions, and the strip $\Omega_2\mathrel{\mathop:}=\mathbb{R}^2\times(-1,1)$ with periodic boundary conditions in the vertical direction. In a first time, we establish a global existence and uniqueness theorem for small initial data in a suitable anisotropic Besov space. Then, we also justify, in a similar functional framework, the singular limit from the anisotropic Navier-Stokes equations to this system.

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Valentin Lemarié. 2025-07-10. The primitive equations for the ocean and atmosphere in anisotropic spaces. https://arxiv.org/abs/2507.07546

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