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The boundary value problems for the scalar Oseen equation. (English) Zbl 1257.31006
Summary: 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 \(C^{2}\)-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.

MSC:
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
35C15 Integral representations of solutions to PDEs
35J25 Boundary value problems for second-order elliptic equations
45B05 Fredholm integral equations
76D07 Stokes and related (Oseen, etc.) flows
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