Journal of the
Korean Mathematical Society JKMS

We present analysis and some computational methods for boundary optimal and feedback control problems for Navier-Stokes equations. We use one example to illustrate our methodology and ideas which are applicable to general control problems for Navier-Stokes equations. First, we discuss the existence of optimal solutions and derive an optimality system of equations from which an optimal solution may be computed. Then we present a gradient type iterative method. Finally, we present some numerical results.

Keywords: flow control, Navier-Stokes equations, finite element methods

MSC numbers: 49A22, 49B22, 65N30