Abstract
The purpose of this article is to prove the existence and uniqueness of the solution to a two-dimensional cell model problem, which describes the Stokes flow of a viscous incompressible fluid in a bounded Lipschitz region past a porous medium and in the presence of a solid core. The flow within the porous medium is described by the Brinkman equation. One uses the continuity of the velocity and traction fields at the fluid–porous interface, while on the exterior boundary of the fluid envelope, as well as on the boundary of the solid core the velocity field satisfies the prescribed Dirichlet conditions. In order to show the desired existence and uniqueness in certain Sobolev spaces, we develop a layer potential approach based on the potential theory for the Stokes and Brinkman equations. In addition, some particular cases are also analysed.
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