The primitive equations for the ocean and atmosphere in anisotropic spaces

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 $Ω_1\mathrel{\mathop:}=(-1,1)^3$ with periodic boundary conditions, and the strip $Ω_2\mathrel{\mathop:}=\mathbb{R}^2\times(-1,1)$ 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.