The exterior Dirichlet and the interior Neumann boundary value problems for the scalar Oseen equation

Abstract

The scalar Oseen equation represents a linearized form of the Navier Stokes equations. We present an explicit potential theory for this equation and solve the exterior Dirichlet and interior Neumann boundary value problems via a boundary integral equations method in spaces of continuous functions on a C 2 -boundary, extending the classical approach for the isotropic selfadjoint Laplace operator to the anisotropic non-selfadjoint scalar Oseen operator.