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On exact controllability for the Navier-Stokes equations

Published online by Cambridge University Press:  15 August 2002

O. Yu. Imanuvilov
O. Yu. Imanuvilov*
Affiliation:
(oleg@kias.kaist.ac.kr)
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Abstract

We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in abounded domain with control distributed in an arbitrary fixed subdomain. The result that we obtain in this paper is as follows.Suppose that we have a given stationary point of the Navier-Stokes equations and our initial condition is sufficiently close to it. Thenthere exists a locally distributed control such that in a given moment of time the solution of the Navier-Stokes equations coincideswith this stationary point.

Keywords

Locally distributed controlNavier-Stokes equations.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 3 , 1998 , pp. 97 - 131
Copyright
© EDP Sciences, SMAI, 1998

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