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.
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.