Asymptotics and vortex patches for the quasigeostrophic approximation

Abstract

We focus in the first part of this article on the explicit estimate, in terms of the Rossby number ɛ, of the convergence speed of the solution of the primitive equations to the unique and global solution of the quasigeostrophic system, with better results when ν = ν ′ . The second part is devoted to the proof of the persistence, when the Rossby number goes to zero, of the structure of tangential regularity for the primitive equations with diffusion and viscosity.