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We study the Dirichlet problem for Stokes equations outside curvilinear open arcs in a half-plane. We prove existence and uniqueness of a classical solution to this problem. We obtain integral representation for a solution in the form of potentials, densities in which can be found as a unique solution of the system of the Fredholm integral equations of the second kind and index zero. The creeping flow of viscous fluid over thin profiles is described by the Dirichlet problem studied in this paper.

The Dirichlet problem for Stokes equations outside open arcs in a half-plane and creeping flow over thin profiles