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Boundary Value Problem for Stationary Stokes Equations with Impermeability Boundary Condition

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We propose two approaches to the study of the boundary value problem for the stationary Stokes equations with impermeability boundary condition. The first approach is classical and is based on a Friedrichs type inequality and a variant of the de Rham theorem. The second approach is based on solving the boundary value problem with the impermeability condition for the system of Poisson equations and decomposition of a Sobolev space into the sum of solenoidal and potential subspaces. We also study the gradient-divergence boundary value problem with impermeability boundary condition and establish the corresponding Ladyzhenskaya–Babushka–Brezzi inequality.

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References

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  1. National Research University “Moscow Power Engineering Institute”, 14, Krasnokazarmennaya St., Moscow, 111250, Russia

    Yu. A. Dubinskii

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  1. Yu. A. Dubinskii
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Correspondence to Yu. A. Dubinskii.

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Dedicated to Nina Nikolaevna Uraltseva

Translated from Problemy Matematicheskogo Analiza 78, January 2015, pp. 75-83.

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Dubinskii, Y.A. Boundary Value Problem for Stationary Stokes Equations with Impermeability Boundary Condition. J Math Sci 207, 195–205 (2015). https://doi.org/10.1007/s10958-015-2365-x

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  • DOI: https://doi.org/10.1007/s10958-015-2365-x

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