Stabilization by Noise of Navier–Stokes Equations

  • Viorel Barbu
Part of the Communications and Control Engineering book series (CCE)


The stochastic stabilization of Navier–Stokes equations is an alternative approach to stabilization techniques described in Chap. 3, which have two important advantages: the simplicity of the stabilizable feedback law and its robustness to (deterministic and stochastic) perturbations. A long time ago, it was observed that the noise might stabilize the finite and infinite-dimensional dynamical systems and several empirical observations in fluid dynamics suggested that noise might have a dissipation effect comparable with increasing the viscosity of fluid. This is exactly what will be rigorously proven here by designing stabilizing noise feedback controller with internal or boundary support.


Stochastic Differential Equation Feedback Controller Stochastic Stabilization Unique Mild Solution Independent Brownian Motion 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Fac. MathematicsAl. I. Cuza UniversityIaşiRomania

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