Evolution Equations and Control Theory (EECT)

Certain questions of feedback stabilization for Navier-Stokes equations

Pages: 109 - 140, Volume 1, Issue 1, June 2012      doi:10.3934/eect.2012.1.109

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Andrei Fursikov - Department of Mechanics & Mathematics, Moscow State University, Moscow 119991, Russian Federation (email)
Alexey V. Gorshkov - Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russian Federation (email)

Abstract: The authors study the stabilization problem for Navier-Stokes and Oseen equations near steady-state solution by feedback control. The cases of control in initial condition (start control) as well as impulse and distributed controls in right side supported in a fixed subdomain of the domain $G$ filled with a fluid are investigated. The cases of bounded and unbounded domain $G$ are considered.

Keywords:  Navier-Stokes equations, stabilization, control, feedback operator, invariant manifold.
Mathematics Subject Classification:  Primary: 93D15, 76D05.

Received: November 2011;      Revised: February 2012;      Available Online: March 2012.