Abstract. 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! Ω Rn; n 2 f2; 3g. The result that we obtained in this paper is as follows. Suppose that v̂(t; x) is a given solution of the Navier-Stokes equations. Let v0(x) be a given initial condition and kv̂(0; )−v0k < " where " is small enough. Then there exists a locally distributed control u; suppu (0; T) ! such that the solution v(t; x) of the Navier-Stokes equations
