In this paper we deal with the local exact controllability of the
Navier-Stokes system with nonlinear Navier-slip boundary
conditions and distributed controls supported in small sets. In a
first step, we prove a Carleman inequality for the linearized
Navier-Stokes system, which leads to null controllability of this
system at any time T>0. Then, fixed point arguments lead to the
deduction of a local result concerning the exact controllability
to the trajectories of the Navier-Stokes system.