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Optimal Feedback Control for Leray and Navier–Stokes Alpha Models

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Abstract

The existence of an optimal feedback control for the Leray alpha model and the Navier–Stokes alpha model is proved. The control of external forces that depend on the fluid velocity is considered. As a result, the control function can be chosen more accurately, since, in this case, it is chosen not from a finite set of available controls, but belongs to the image of a multivalued mapping. The existence of an optimal solution minimizing a specified bounded lower semicontinuous quality functional is proved by applying the topological approximation method for studying hydrodynamic problems.

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Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project no. 14.Z50.31.0037) and by a grant from the President of the Russian Federation for the state support of young Russian scientists (MK-2213.2018.1, agreement 075-02-2018-339).

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Authors and Affiliations

  1. Voronezh State University, 394006, Voronezh, Russia

    A. V. Zvyagin

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  1. A. V. Zvyagin
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Correspondence to A. V. Zvyagin.

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Translated by I. Ruzanova

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Zvyagin, A.V. Optimal Feedback Control for Leray and Navier–Stokes Alpha Models. Dokl. Math. 99, 299–302 (2019). https://doi.org/10.1134/S1064562419030190

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  • DOI: https://doi.org/10.1134/S1064562419030190

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