Uniqueness for a stochastic inviscid dyadic model

Barbato, D.; Flandoli, F.; Morandin, F.

doi:10.1090/S0002-9939-10-10318-9

Uniqueness for a stochastic inviscid dyadic model
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by D. Barbato, F. Flandoli and F. Morandin PDF

Proc. Amer. Math. Soc. 138 (2010), 2607-2617 Request permission

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.

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