  The purpose of this paper is to obtain existence and uniqueness results in
weighted Sobolev spaces for transmission problems for the non-linear
Darcy-Forchheimer-Brinkman system and the linear Stokes system in two
complementary Lipschitz domains in ${\mathbb R}^3$, one of them is a bounded
Lipschitz domain $\Omega $ with connected boundary, and another one is the
exterior Lipschitz domain ${\mathbb R}^3\setminus \overline{\Omega }$. 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.
