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The boundary value problems for the scalar Oseen equation



The scalar Oseen equation represents a linearized form of the Navier Stokes equations, well-known in hydrodynamics. In the present paper we develop an explicit potential theory for this equation and solve the interior and exterior Oseen Dirichlet and Oseen Neumann boundary value problems via a boundary integral equation method in spaces of continuous functions on a C2-boundary, extending the classical approach for the isotropic selfadjoint Laplace operator to the anisotropic non-selfadjoint scalar Oseen operator. It turns out that the solution to all boundary value problems can be presented by boundary potentials with source densities constructed as uniquely determined solutions of boundary integral equations.