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One designs an internal stabilizing feedback controller, for the Navier-Stokes equations, which steers, in finite time, the initial value $X_o$ in $X_e+\mathcal{X}_s$, where $X_e$ is any equilibrium solution and $\mathcal{X}_s$ is a finite codimensional space, consisting of stable modes.

Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension