  In this paper, we deal with the existence of insensitizing controls for the
Navier-Stokes equations in a bounded domain with Dirichlet boundary conditions.
We prove that there exist controls insensitizing the $L^2$ -norm of the
observation of the solution in an open subset $\mathcal{O}$ of the domain,
under suitable assumptions on the data.
  This problem is equivalent to an exact controllability result for a cascade
system. First we prove a global Carleman inequality for the linearized
Navier-Stokes system with right-hand side, which leads to the null
controllability at any time $T>0$. Then, we deduce a local null controllability
result for the cascade system.
