Long-term behaviour of the primitive equations: Convergence to the Ekman spiral

In this talk we investigate the long-term behaviour of the 3D incompressible, primitive equations with wind-driven boundary conditions and Coriolis force in the regime where the Reynolds number is small in comparison to the Coriolis force. We show that every solution converges exponentially fast to the Ekman spiral as $t \to + \infty$. In particular, this implies that the Ekman spiral is the unique equilibrium of the system.