For the deterministic dyadic model of turbulence, there are examples of initial conditions in l^2 which have more than one solution. The aim of this paper is to prove that uniqueness, for all l^2 initial conditions, is restored when a suitable multiplicative noise is introduced. The noise is formally energy preserving. Uniqueness is understood in the weak probabilistic sense.
Uniqueness for a Stochastic Inviscid Dyadic Model / D., Barbato; F., Flandoli; Morandin, Francesco. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 138:(2010), pp. 2607-2617. [10.1090/S0002-9939-10-10318-9]
Uniqueness for a Stochastic Inviscid Dyadic Model
MORANDIN, Francesco
2010-01-01
Abstract
For the deterministic dyadic model of turbulence, there are examples of initial conditions in l^2 which have more than one solution. The aim of this paper is to prove that uniqueness, for all l^2 initial conditions, is restored when a suitable multiplicative noise is introduced. The noise is formally energy preserving. Uniqueness is understood in the weak probabilistic sense.File in questo prodotto:
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