Stabilizing a solution of the 2D Navier-Stokes system in the exterior of a bounded domain by means of a control on the boundary

The problem of stabilizing a solution of the 2D Navier-Stokes system defined in the exterior of a bounded domain with smooth boundary is investigated. For a given initial velocity field a control on the boundary of the domain must be constructed such that the solution stabilizes to a prescribed vortex solution or trivial solution at the rate of 1/tk. On the way, related questions are investigated, concerning the behaviour of the spectrum of an operator under a relatively compact perturbation and the existence of attracting invariant manifolds. Bibliography: 21 titles.