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Uniqueness of the generators of the 2D Euler and Navier-Stokes flows

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  • Albeverio, S.
  • Barbu, V.
  • Ferrario, B.

Abstract

A uniqueness result is proven for the infinitesimal generator associated with the 2D Euler flow with periodic boundary conditions in the space L2([mu]) with respect to the natural Gibbs measure [mu] given by the enstrophy. This result remains true for the generator of the stochastic process associated with a 2D Navier-Stokes equation perturbed by a space-time Gaussian white noise force. The corresponding Liouville operator N defined on the space of smooth cylinder bounded functions has a unique skew-adjoint m-dissipative extension in the class of closed operators in L2([mu])xV' where .

Suggested Citation

  • Albeverio, S. & Barbu, V. & Ferrario, B., 2008. "Uniqueness of the generators of the 2D Euler and Navier-Stokes flows," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2071-2084, November.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:11:p:2071-2084
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    1. Albeverio, Sergio & Høegh-Krohn, Raphael, 1989. "Stochastic flows with stationary distribution for two-dimensional inviscid fluids," Stochastic Processes and their Applications, Elsevier, vol. 31(1), pages 1-31, March.
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    Cited by:

    1. Martin Sauer, 2016. "$$L^1$$ L 1 -Uniqueness of Kolmogorov Operators Associated with Two-Dimensional Stochastic Navier–Stokes Coriolis Equations with Space–Time White Noise," Journal of Theoretical Probability, Springer, vol. 29(2), pages 569-589, June.

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    1. Martin Sauer, 2016. "$$L^1$$ L 1 -Uniqueness of Kolmogorov Operators Associated with Two-Dimensional Stochastic Navier–Stokes Coriolis Equations with Space–Time White Noise," Journal of Theoretical Probability, Springer, vol. 29(2), pages 569-589, June.

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