A Numerical Approach to the Control and Stabilization of Advection-Diffusion Systems: Application to Viscous Drag Reduction

In this article we investigate computational methods for the control and stabilization of systems modeled by parabolic equations of the advection-reaction-difTusion type and by the Navier-Stokes equations for incompressible viscous fluids. For the first class of control problems wc shall discuss open loop control methods and closed loop methods a la Riccati. Concerning the second class of problems we shall consider the Dirichlet boundary control of low around cylinders and attempt to reduce the viscous drag. The results of numerical experiments will validate the computational methods described in this article.