# American Institute of Mathematical Sciences

June  2012, 1(1): 1-16. doi: 10.3934/eect.2012.1.1

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

 1 Octav Mayer Institute of Mathematics (Romanian Academy), Bd. Carol I, no. 8, Iaşi 700505, Romania 2 Octav Mayer Institute of Mathematics (Romanian Academy), and Alexandru Ioan Cuza University (Department of Mathematics), Bd. Carol I, no. 8, Iaşi 700505, Romania

Received  August 2011 Revised  October 2011 Published  March 2012

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.
Citation: Viorel Barbu, Ionuţ Munteanu. Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension. Evolution Equations & Control Theory, 2012, 1 (1) : 1-16. doi: 10.3934/eect.2012.1.1
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