Asymptotic analysis for the 3D primitive equations in a channel

Abstract

In this article, we give an asymptotic expansion, with respect to the viscosity which is considered here to be small, of the solution of the 3D linearized Primitive Equations (EPs) in a channel with lateral periodicity. A rigorous convergence result, in some physically relevant space, is proven. This allows, among other consequences, to confirm the natural choice of the non-local boundary conditions for the non-viscous PEs.