Kurt Frischmuth, Jürgen Roßmann
On the Dirichlet Problem for the Ekman Equation
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

35J20 Variational methods for second-order, elliptic equations

35J25 Boundary value problems for second-order, elliptic equations

Abstract: 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.
Keywords: Second order elliptic equations, asymptotics, hydrodynamics