Navier-Stokes equations with Coriolis force and vanishing vertical viscosity

We consider the 3-D Navier-Stokes equations with Coriolis force of order 1/epsilon and vanishing vertical viscosity of order epsilon. For suitable initial data, we prove some global or-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 non-homogeneous strain; in this case, we compute and justify the corrector.