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. email@example.com
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