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Dirichlet problem for the Stokes equations outside open curves on the plane

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Abstract

The Dirichlet problem for the Stokes equations outside open curves on the plane is studied. The existence and uniqueness of a solution is proved. An integral representation for the solution is obtained in the form of potentials whose densities are determined from a uniquely solvable system of Fredholm integral equations of the second kind. The singularities of derivatives of the velocities at the endpoints of the open curves are analyzed. A closed-form solution of the problem is constructed for the case in which the open curves are straight line segments.

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Authors and Affiliations

  1. Institute for Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    P. A. Krutitskii

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  1. P. A. Krutitskii
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Original Russian Text © P.A. Krutitskii, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 9, pp. 1161–1174.

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Krutitskii, P.A. Dirichlet problem for the Stokes equations outside open curves on the plane. Diff Equat 44, 1203–1217 (2008). https://doi.org/10.1134/S0012266108090024

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  • DOI: https://doi.org/10.1134/S0012266108090024

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