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February  2004, 10(1&2): 289-314. doi: 10.3934/dcds.2004.10.289

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

A. V. Fursikov 1,

1. 

Department of Mechanics and Mathematics, Moscow State University, 119899 Moscow, Russian Federation

Received  November 2001 Revised  December 2002 Published  October 2003

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: Carleman estimate, stabilization, invariant manifold., Navier-Stokes equations, extension operator.
Mathematics Subject Classification: 93D15, 76D0.
Citation: A. V. Fursikov. Stabilization for the 3D Navier-Stokes system by feedback boundary control. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 289-314. doi: 10.3934/dcds.2004.10.289
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