The Stationary Navier-Stokes System in Nonsmooth Manifolds: The Poisson Problem in Lipschitz and C1 Domains

We consider the linearized version of the stationary Navier-Stokes equations on a subdomain of a smooth, compact Riemannian manifold M. The emphasis is on regularity: the boundary of is assumed to be only C¹ and even Lipschitz, and the data are selected from appropriate Sobolev-Besov scales. Our approach relies on the method of boundary integral equations, suitably adapted to the variable-coefficient setting we are considering here. Applications to the stationary, nonlinear Navier-Stokes equations in this context are also discussed.