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.

References in corpus (3)

• Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift
• A dyadic model on a tree
• Stochastic inviscid shell models: well-posedness and anomalous dissipation

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• Regularized vortex approximation for 2D Euler equations with transport noise
• A stationary solution for the mixed turbulence shell model
• Stationary solutions for dyadic mixed model of the Euler equation. A complete spectrum