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## Oseen equations

A body with an arbitrary shape is moving in a fluid of density  with an velocity  denotes the distance from the body. Further  denotes the velocity of the fluid and  the hydrostatical oressure. Oseen equations for flow due to a moving body at small Reynolds numbers is given as follows:
The second relation models the incompressibility of the fluid. Boundary conditions for a rigid body are given by:
For further information on the model have a look in G.K.Batchelor (2000) An introduction to fluid dynamics Cambridge Mathematical Library. It can be seen as an exterior Dirichlet problem in  where  is simple connected domain.

This problem is discussed as direct and inverse problem. A single-layer potential approach in a Sobolev setting with a lot of interesting references is treated in:

A late reference: R. Kress and Mayer S. (2000) An Inverse Boundary Value Problem for the Oseen Equation MMAS 23, 103-120.

collected and worked out by Wolfgang Sprößig, TU-Bergakademie Freiberg