Boundary velocity suboptimal control of incompressible flow in cylindrically perforated domain

In this paper we study an optimal boundary control problem for the 3D steady-state Navier-Stokes equation in a cylindrically perforated domain Ωᵋ The control is the boundary velocity field supported on the ‘vertical’ sides of thin cylinders. We minimize the vorticity of viscous flow through thick perforated domain. We show that an optimal solution to some limit problem in a non-perforated domain can be used as basis for the construction of suboptimal controls for the original control problem. It is worth noticing that the limit problem may take the form of either a variational calculation problem or an optimal control problem for Brinkman’s law with another cost functional, depending on the cross-size of thin cylinders