Optimal control of a cylinder rotating in a viscous fluid

Under consideration is the axisymmetric problem of optimal boundary control of a mechanical system consisting of two coaxial cylinders and an incompressible viscous fluid filling the region between them. The control parameter is the angular velocity of the outer cylinder. The goal is to stop the interior cylinder at a prescribed time with minimal energy expense. We prove that the problem is uniquely solvable and obtain the optimality system.