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

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.

KEYWORDS:

• Existence
• Navier-Stokes-Voigt equations
• necessary optimality conditions
• optimal control
• sufficient optimality conditions

MATHEMATICS SUBJECT CLASSIFICATION:

• 49J20
• 49K20
• 76D55
• 35Q35

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.