Optimal boundary control of nonsteady incompressible flow with an application to viscous drag reduction

摘要

The objective of this study is to characterize the boundary velocity distribution that in some sense gives the lowest viscous drag for viscous, incompressible flows. The case is considered where the control is explicitly constrained. Necessary conditions are presented for optimal controls for the Navier-Stokes equations in a bounded region. An application to reducing viscous drag by blowing and suction is discussed. The first part of the study considers static control; the second part is concerned with time-varying optimal controls.