Damping effects in boundary layers for rotating fluids with small viscosity

The goal of this paper is to study the system of rotating fluids between two infinite parallel plates with Dirichlet boundary conditions and with small viscosity which vanishes when the Rossby number goes to zero. We want to improve the convergence result of [16] and show the global in time convergence of the weak solution of the system of rotating fluids towards the solution of a two-dimensional damped Euler system with three components, using the decay in time of the H^s -norm (s > 2) of the limiting solution