An optimal boundary control problem for the Navier-Stokes equations is presented. The control is the velocity on the boundary, which is constrained to lie in a closed, convex subset of H1/2 of the boundary. A necessary condition for optimality is derived. Computations are done when the control set is actually finite-dimensional, resulting in all application to viscous drag reduction.
Gunzberger, M. D.,
& Svobodny, T.
(1992). Boundary Velocity Control of Incompressible-Flow with an Application to Viscous Drag Reduction. SIAM Journal on Control and Optimization, 30 (1), 167-181.