Transmission Problems for the Navier–Stokes and Darcy–Forchheimer–Brinkman Systems in Lipschitz Domains on Compact Riemannian Manifolds

Abstract

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.