Homogenization and corrector result of optimal control problem for Stokes system

Abstract

This article introduces the boundary optimal control problem in an N-dimensional domain governed by the stationary Stokes equations. Controls are applied to the states through Neumann data on the boundary. The aim of this paper is to study the asymptotic behavior of optimal control and states and identify the limit optimal control problem in the framework of the two-scale convergence. Finally, strong convergence of L 2 -cost functional and a corrector result for velocities is proved.