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Abstract

We prove the existence of solution in the class $H^2(\Omega) \times H^1(\Omega)$ to the steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with boundary of class $H^{5/2}$. The method is to regularize a weak solution obtained via the Galerkin method. The problem of regularization is reduced to the problem of solvability of a certain transport equation by application of the Helmholtz decomposition. The method works under an additional assumption on the geometry of the boundary.