  Given a nonstationary trajectory of the Navier-Stokes system, a
finite-dimensional feedback boundary controller stabilizing locally the system
to the given trajectory is derived. Moreover the controller is supported in a
given open subset of the boundary of the domain containing the fluid.
  In a first step a controller is derived that stabilizes the linear
Oseen-Stokes system "around the given trajectory" to zero; for that a corollary
of a suitable truncated boundary observability inequality, the regularizing
property for the system, and some standard techniques of the optimal control
theory are used. Then it is shown that the same controller also stabilizes,
locally, the Navier-Stokes system to the given trajectory.
