Internal Stabilization by Noise of the Navier--Stokes Equation

نویسندگان

  • Viorel Barbu
  • Giuseppe Da Prato
چکیده

One shows that the Navier-Stokes equation in O⊂Rd, d = 2, 3, around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller V (t, ξ) = ∑N i=1 Vi(t)ψi(ξ)β̇i(t), ξ ∈ O, where {βi}i=1 are independent Brownian motions and {ψi}i=1 is a system of functions on O with support in an arbitrary open subset O0 ⊂ O. The stochastic control input {Vi}i=1 is found in feedback form. The corresponding result for the linearized Navier-Stokes equation was established in [2]. 2000 Mathematics Subject Classification AMS: 35Q30, 60H15, 35B40

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عنوان ژورنال:
  • SIAM J. Control and Optimization

دوره 49  شماره 

صفحات  -

تاریخ انتشار 2011