Issue |
ESAIM: COCV
Volume 6, 2001
|
|
---|---|---|
Page(s) | 39 - 72 | |
DOI | https://doi.org/10.1051/cocv:2001103 | |
Published online | 15 August 2002 |
Remarks on exact controllability for the Navier-Stokes equations
Department of Mathematics, Iowa State University,
400 Carver Hall, Ames, IA 50011-2064, U.S.A.; vika@iastate.edu.
Received:
27
August
1999
Revised:
29
February
2000
Revised:
28
September
2000
We study the local exact
controllability problem for the Navier-Stokes equations
that describe an incompressible fluid flow in a bounded domain
Ω with control distributed in a subdomain .
The result that we obtained in this paper is
as follows. Suppose that
is a given
solution of the
Navier-Stokes equations. Let
be a given initial condition
and
where ε is small enough. Then there
exists a locally distributed control
such that the solution v(t,x) of
the Navier-Stokes equations:
coincides with
at the instant T :
.
Résumé
On étudie le problème de contrôlabilité locale exacte
pour les équations de Navier-Stokes incompressibles
dans un domaine borné avec un contrôle
réparti dans un sous-domaine
On obtient
le résultat suivant. Supposons que
soit
une solution des équations de Navier-Stokes
et
une condition initiale telle que
pour ε assez petit. On montre alors qu'il existe un
contrôle localement réparti
tel que la solution v(t,x) des équations de Navier-Stokes:
coïncide avec
au temps T:
Mathematics Subject Classification: 35K10 / 35K55 / 35K60 / 93B05 / 93C10 / 93C20
Key words: Locally distributed control / Navier-Stokes system.
© EDP Sciences, SMAI, 2001
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