The Navier-Stokes equations are the fundamental model for the mathematical analysis of incompressible viscous fluids. In this text, a modification of this system of partial differential equations representing the situation of geophysical flows is investigated. An important mathematical model of geophysical boundary layers is the Ekman spiral, which is a stationary solution of the modified Navier-Stokes equations. Its long-time behaviour is of certain interest in natural sciences. Here, the stability of the Ekman spiral is shown in three-dimensional halfspaces and infinite layers in the case of a small Reynolds number of the according hydrodynamical system. The problem of maximal regularity of the Stokes operator in bounded and exterior domains with smooth boundary is also discussed