Nonlinear Stability of Ekman boundary layers

Abstract

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