  We consider the Navier-Stokes system in a bounded domain with a smooth
boundary. Given a sufficiently regular time-dependent global solution, we
construct a finite-dimensional feedback control that is supported by a given
open set and stabilizes the linearized equation. The proof of this fact is
based on a truncated observability inequality, the regularizing property for
the linearized equation, and some standard techniques of the optimal control
theory. We then show that the control constructed for the linear problem
stabilizes locally also the full Navier-Stokes system.
