Rotating fluid at high Rossby number driven by a surface stress: existence and convergence

Abstract

We consider the 3-D Navier-Stokes equations with Coriolis force of order $\frac{1}{\epsilon}$ and vanishing vertical viscosity of order $\epsilon$. For suitable initial data, we prove some long-time existence results. Moreover, we obtain convergence as $\epsilon$ goes to 0 to the 2-D Navier-Stokes equations. We deal with periodic boundary conditions and nonhomogeneous stress. In this case, we compute and justify the corrector.