Remarks on exact controllability for the Navier-Stokes equations

We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain Ω with control distributed in a subdomain . The result that we obtained in this paper is as follows. Suppose that is a given solution of the Navier-Stokes equations. Let be a given initial condition and where ε is small enough. Then there exists a locally distributed control such that the solution v(t,x) of the Navier-Stokes equations: coincides with at the instant T : .