Stabilization from the boundary of solution for Navier-Stokes system: solvability and justification of numerical simulation

A stabilization method for solution of Navier-Stokes system near steady-state (unstable) solution is expounded. Stabilization is done by a control from the boundary of the domain where equations are defined. Important point of the stabilization problem which we study in this paper is justification of possibility for numerical simulation. We solve the problem choosing feedback control.