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navier − stokes equation

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative Gaussian noise ∗
Viorel Barbu
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 4 / October 2013

Published online by Cambridge University Press:

04 July 2013, pp. 1055-1063

Print publication:

October 2013
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The parabolic equations driven by linearly multiplicative Gaussian noise are stabilizable in probability by linear feedback controllers with support in a suitably chosen open subset of the domain. This procedure extends to Navier − Stokes equations with multiplicative noise. The exact controllability is also discussed.