Hydrostatic approximation of the 2D primitive equations in a thin strip

Abstract

We prove the global wellposedness of the 2D non-rotating primitive equations with noslip boundary conditions in a thin strip of width ε for small data which are analytic in the tangential direction. We also prove that the hydrostatic limit (when ε → 0) is a couple of a Prandtl-like system for the velocity with a transport-diffusion equation for the temperature.