Uniqueness for a Stochastic Inviscid Dyadic Model

Mathematics – Probability

Scientific paper

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13 pages, no figures. Submitted to the Proceedings of the American Mathematical Society

Scientific paper

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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