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.
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Kurt Frischmuth, Jürgen Rossmann, On the Dirichlet Problem for the Ekman Equation. Z. Anal. Anwend. 15 (1996), no. 2, pp. 329–343DOI 10.4171/ZAA/703