Layer potential analysis for a Dirichlet‐transmission problem in Lipschitz domains in ℝn

Abstract

AbstractIn this paper we obtain the existence and uniqueness in some Sobolev and Lp spaces for a Dirichlet‐transmission problem for the Stokes and Brinkman equations on Lipschitz domains in ℝn, n > 3. In the particular case n = 3 this problem describes the Stokes flow of a viscous incompressible fluid past a porous particle and in presence of a solid core. The flow within the porous particle is described by the Brinkman equation. In order to obtain the desired existence and uniqueness result, we use an indirect boundary integral formulation based on the layer potential theory for both Brinkman and Stokes equations. Some special cases, which refer to the Stokes flow past a porous particle with large permeability, respectively low permeability, are also analyzed.