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On some optimal control problems connected with the Navier-Stokes system

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Abstract

We consider problems of the form

$$\left\{ \begin{gathered} J(y) \to \inf : \hfill \\ L(y) = u, \left\| u \right\| \leqslant M, y(0) = 0, y(T) = v, \hfill \\\end{gathered} \right.$$

whereL is the operator of the Navier-Stokes system. We obtain theorems for existence of a solution and necessary and sufficient conditions for an extremum. We also study the uniqueness of the solution and construct the asymptotics of the solution in terms of the parameter M. Bibliography: 11 titles.

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Authors
  1. O. Yu. Emanuilov
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Additional information

Translated fromTrudy Seminara imeni I. G. Petrovskogo, No. 15, pp. 108–127, 1991.

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Emanuilov, O.Y. On some optimal control problems connected with the Navier-Stokes system. J Math Sci 60, 1725–1741 (1992). https://doi.org/10.1007/BF01102586

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  • DOI: https://doi.org/10.1007/BF01102586

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