Transmission problems for the Navier-Stokes and   Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian   manifolds
  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. 
Mirela Kohr, Sergey E. Mikhailov, Wolfgang L. Wendland
math.AP