A uniqueness result is proven for the infinitesimal generator associated with the 2D Euler flow with periodic boundary conditions in the space of square summable functions with respect to the natural Gibbs measure μ 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 a particular class of closed operators.
Uniqueness of the generators of the 2D Euler and Navier-Stokes flows
FERRARIO, BENEDETTA
2008
Abstract
A uniqueness result is proven for the infinitesimal generator associated with the 2D Euler flow with periodic boundary conditions in the space of square summable functions with respect to the natural Gibbs measure μ 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 a particular class of closed operators.File in questo prodotto:
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