Uniqueness for an inviscid stochastic dyadic model on a tree

Abstract

In this paper we prove that the lack of uniqueness for solutions of the tree dyadic model of turbulence is overcome with the introduction of a suitable noise. The uniqueness is a weak probabilistic uniqueness for all \(l^2\)-initial conditions and is proven using a technique relying on the properties of the \(q\)-matrix associated to a continuous time Markov chain.