Boundary optimal feedback controller for time-periodic Stokes–Oseen flows

This work considered the Dirichlet boundary optimal control of time-periodic Stokes–Oseen equations. The existence of optimal solution and maximum principle are obtained without assuming that the normal component of the control is equal to zero. Moreover, we get the regularity result of the optimal solution via the Euler–Lagrange system. The existence of solution to the HJB equation is proved. The feedback form of the optimal controller is given, and with this feedback controller, we can get for the solution to the periodic Navier–Stokes equations the property of continuous dependence on the outer force term.