From anisotropic Navier-Stokes equations to primitive equations for the ocean and atmosphere

We study the well-posedness of the primitive equations for the ocean and atmosphere on two particular domains : a bounded domain Ω₁ := (-1, 1)³ with periodic boundary conditions and the strip Ω₂ := R² × (-1, 1) with a periodic boundary condition for the vertical coordinate. An existence theorem for global solutions on a suitable Besov space is derived. Then, in a second step, we rigorously justify the passage to the limit from the rescaled anisotropic Navier-Stokes equations to these primitive equations in the same functional framework as that found for the solutions of the primitive equations.