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On the uniqueness and stability of solutions of extremal problems for the stationary Navier-Stokes equations

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Abstract

We consider inverse extremal problems for the stationary Navier-Stokes equations. In these problems, one seeks an unknown vector function occurring in the Dirichlet boundary condition for the velocity and the solution of the considered boundary value problem on the basis of the minimization of some performance functional. We derive new a priori estimates for the solutions of the considered extremal problems and use them to prove theorems of the local uniqueness and stability of solutions for specific performance functionals.

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Authors and Affiliations

  1. Institute for Applied Mathematics, Far East Branch of the Russian Academy of Sciences, Vladivostok, Russia

    G. V. Alekseev & R. V. Brizitskii

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  1. G. V. Alekseev
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  2. R. V. Brizitskii
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Original Russian Text © G.V. Alekseev, R.V. Brizitskii, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 1, pp. 68–79.

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Alekseev, G.V., Brizitskii, R.V. On the uniqueness and stability of solutions of extremal problems for the stationary Navier-Stokes equations. Diff Equat 46, 70–82 (2010). https://doi.org/10.1134/S0012266110010088

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  • DOI: https://doi.org/10.1134/S0012266110010088

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