*PN* 95/7 TI eng: On the Dirichlet Problem for the Ekman Equation dt: Zum Dirichlet Problem f"ur die Ekman-Gleichung AU Frischmuth, Kurt; Rossmann, J"urgen SO Preprint 95/7, ISSN 0948-1028 LA englisch AB The Ekman partial differential equation for the streamfunktion of turbulent mass flow in shallow and small sized surface water is 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. CC 35J20 Second order elliptic equations, variational methods 35J25 Second order elliptic equations, boundary value problems UT Second order elliptic equations, asymptotics, hydrodynamics