Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Stabilization for the 3D Navier-Stokes system by feedback boundary control

Pages: 289 - 314, Volume 10, Issue 1/2, January/February 2004      doi:10.3934/dcds.2004.10.289

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A. V. Fursikov - Department of Mechanics and Mathematics, Moscow State University, 119899 Moscow, Russian Federation (email)

Abstract: We study the problem of stabilization a solution to 3D Navier-Stokes system given in a bounded domain $\Omega$. This stabilization is carried out with help of feedback control defined on a part $\Gamma$ of boundary $\partial \Omega$. We assume that $\Gamma$ is closed 2D manifold without boundary. Here we continuer investigation begun in [6], [7] where stabilization problem for parabolic equation and for 2D Navier-Stokes system was studied.

Keywords:  Navier-Stokes equations, stabilization, Carleman estimate, extension operator, invariant manifold.
Mathematics Subject Classification:  93D15, 76D05.

Received: November 2001;      Revised: December 2002;      Available Online: October 2003.