Nonlinear stability of Ekman boundary layers

Consider the initial value problem for the three-dimensional Navier-Stokes equations with rotation in the half-space ³+ subject to Dirichlet boundary conditions as well as the Ekman spiral, which is a stationary solution to the above equations. It is proved that the Ekman spiral is nonlinearly stable with respect to L²-perturbations provided that the corresponding Reynolds number is small enough. Moreover, the decay rate can be computed in terms of the decay of the corresponding linear problem.