Local Exact Controllability of the Navier--Stokes Equations with the Condition on the Pressure on Parts of the Boundary

Abstract. In this paper we prove a local exact controllability of the Navier–Stokes equations with the condition on the pressure on parts of the boundary. The local exact controllability is proved by using a global Carleman inequality and an estimate of an equation adjoint to a linearized Navier– Stokes equation with the nonstandard boundary condition. We also obtain the null controllability of the linearized system by controls acting on an arbitrarily given subdomain.