Integral potential method for a transmission problem with Lipschitz interface in R-3 for the Stokes and Darcy-Forchheimer-Brinkman PDE systems

摘要

The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the nonlinear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R-3, one of them is a bounded Lipschitz domain Omega with connected boundary, and the other one is the exterior Lipschitz domain R-3 \ (Omega) over bar. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces.