On the Dirichlet Problem for the Ekman Equation

Abstract

The Ekman partial differential equation for the stream function of turbulent mass flow in shallow and small-sized surface waters are discussed. The Dirichlet problem for the Ekman equation is shown to be well-posed in a weighted Sobolev space. Conditions for the existence of classical solutions are given. The dependence of regularity and asymptotics of the solution on the properties of the depth profile are studied.