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

Pages: 1 - 16, Volume 1, Issue 1, June 2012      doi:10.3934/eect.2012.1.1

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Viorel Barbu - Octav Mayer Institute of Mathematics (Romanian Academy), Bd. Carol I, no. 8, Iaşi 700505, Romania (email)
Ionuţ Munteanu - Octav Mayer Institute of Mathematics (Romanian Academy), and Alexandru Ioan Cuza University (Department of Mathematics), Bd. Carol I, no. 8, Iaşi 700505, Romania (email)

Abstract: 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.

Keywords:  Navier-Stokes equation, Oseen-Stokes system, feedback controller, eigenvalue, steady state solution.
Mathematics Subject Classification:  Primary: 93B52, 93C20, 93D15; Secondary: 35Q30, 76D55.

Received: August 2011;      Revised: October 2011;      Available Online: March 2012.

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