Insensitizing controls for the Navier–Stokes equations

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 L2-norm of the observation of the solution in an open subset 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.