Abstract:
This article considers an optimal control problem for the stationary
Stokes system in a three-dimensional domain with a highly oscillating boundary. The controls are acting on the state through the Neumann data on the oscillating part of the boundary with appropriate
scaling parameters εα with α ≥ 1. The periodic unfolding operators
are used to characterize the optimal controls. Using the unfolding
operators, we analyse the asymptotic behaviour of the optimal control problem under consideration. For α = 1, the limit optimal control problem has both boundary and interior controls. For α > 1, the
limit optimal control problem has only boundary controls.
