  The purpose of this paper is to study boundary value problems of transmission
type for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in two
complementary Lipschitz domains on a compact Riemannian manifold of dimension 2
or 3. We exploit a layer potential method combined with a fixed point theorem
in order to show existence and uniqueness results when the given data are
suitably small in $L^2$-based Sobolev spaces.
