Ekman boundary layers in a domain with topography

We investigate the asymptotic behaviour of fast rotating incompressible fluids with vanishing viscosity, in a three dimensional domain with topography including the case of land area. Assuming the initial data is well-prepared, we prove a convergence theorem of the velocity fields to a two-dimensional vector field solving a linear, damped ordinary differential equation. The proof is based on a weak-strong uniqueness argument, combined with an abstract result implying that the weak convergence of a family of weak solutions to the Navier-Stokes-Coriolis system can be translated into a form of uniform-in-time convergence. This argument yields strong convergence of the velocity fields, without a precise rate though.