  We study the well-posedness of the primitive equations for the ocean and
atmosphere on two particular domains : a bounded domain $\Omega_1 := (-1, 1)^3$
with periodic boundary conditions and the strip $\Omega_2 := \mathbb{R}^2
\times (-1, 1)$ 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.
