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

S. Albeverio, V. Barbu and B. Ferrario

Stochastic Processes and their Applications, 2008, vol. 118, issue 11, 2071-2084

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 .

Keywords: Euler; and; Navier-Stokes; flow; Invariant; measure; Liouville; and; Kolmogorov; generators (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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