Uniqueness for a Stochastic Inviscid Dyadic Model

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.

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