Boundary Velocity Control of Incompressible Flow with an Application to Viscous Drag Reduction

Abstract

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 $H^{{1 / 2}} $ of the boundary. A necessary condition for optimality is derived. Computations are done when the control set is actually finite-dimensional, resulting in an application to viscous drag reduction.