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Original Articles

Optimal Control of the Instationary Three Dimensional Navier-Stokes-Voigt Equations

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Pages 415-439 | Received 10 Aug 2015, Accepted 25 Dec 2015, Published online: 12 Apr 2016
 

ABSTRACT

We study an optimal control problem with quadratic objective functional for the three dimensional Navier-Stokes-Voigt equations in bounded domains. We show the existence of optimal solutions, the necessary optimality conditions and the sufficient optimality conditions. The second-order optimality conditions obtained in the article seem to be optimal.

MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgements

The authors would like to thank the reviewers for their helpful comments and suggestions, which improved the presentation of the article. This work was completed while the first author was visiting the Vietnam Institute of Advanced Study in Mathematics (VIASM). He would like to thank the Institute for its hospitality.

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