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In this paper we present a new proof of the null controllability property for the Stokes system. The proof is based on a new spectral inequality for the eigenfunctions of the Stokes operator. As a consequence, we obtain the cost of the null controllability for the Stokes system of order e C / T , when T is small, i.e. , the same order in time as for the heat equation.

Spectral inequality and optimal cost of controllability for the Stokes system