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 1ε and vanishing vertical viscosity of order ε. For suitable initial data, we prove some long-time existence results. Moreover, we obtain convergence as ε goes to 0 to the 2-D Navier-Stokes equations. We deal with periodic boundary conditions and non-homogeneous stress. In this case, we compute and justify the corrector