Optimal Control of Time-Periodic Navier-Stokes-Voigt Equations

Abstract

We consider a quadratic optimal control problem for the 3D Navier-Stokes-Voigt equations with periodic inputs. We prove the existence of optimal solutions, then establish necessary and sufficient optimality conditions. We also define semidiscrete-in-time approximations for the optimal control problem and then prove the existence of a subsequence that converges to an optimal solution.

Keywords:

• Convergence
• existence
• Navier-Stokes-Voigt equations
• optimality conditions
• periodic optimal control
• semidiscrete-in-time approximations

2010 Mathematics Subject Classification:

• 76D55
• 35Q35
• 49J20
• 49K20

Additional information

Funding

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2018.303.