| Issue |
ESAIM: COCV
Volume 17, Number 1, January-March 2011
|
|
|---|---|---|
| Page(s) | 117 - 130 | |
| DOI | https://doi.org/10.1051/cocv/2009042 | |
| Published online | 30 October 2009 | |
The internal stabilization by noise of the linearized Navier-Stokes equation*
Al.I. Cuza University and Octav Mayer Institute of Mathematics of Romanian Academy, Iaşi, Romania. vb41@uaic.ro
Received:
3
January
2009
Revised:
17
June
2009
Revised:
23
July
2009
One shows that the linearized Navier-Stokes equation in
, around an unstable equilibrium
solution is exponentially stabilizable in probability by an
internal noise controller 
, 
, where 
are
independent Brownian motions in a probability space and
is a system of functions on 
with
support in an arbitrary open subset 
. The
stochastic control input 
is found in feedback
form. One constructs also a tangential boundary noise controller
which exponentially stabilizes in probability the equilibrium
solution.
Mathematics Subject Classification: 35Q30 / 60H15 / 35B40
Key words: Navier-Stokes equation / feedback controller / stochastic process / Stokes-Oseen operator
© EDP Sciences, SMAI, 2009
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