The primitive equations for the ocean and atmosphere in anisotropic spaces

TL;DR

This paper proves global existence and uniqueness of solutions for the primitive equations in anisotropic spaces and justifies the limit from Navier-Stokes equations, enhancing understanding of ocean and atmosphere modeling.

Contribution

It establishes well-posedness and singular limit results for primitive equations in anisotropic Besov spaces, a novel functional framework for these models.

Findings

Global existence and uniqueness for small initial data.

Justification of the singular limit from anisotropic Navier-Stokes.

Analysis on specific domains with periodic boundary conditions.

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.