Anomalous dissipation in a stochastic inviscid dyadic model

TL;DR

This paper demonstrates that a stochastic inviscid dyadic model of turbulence exhibits energy dissipation despite formal conservation laws, implying the non-existence of global regular solutions, using probabilistic analysis of a birth-death process.

Contribution

It introduces a stochastic version of the inviscid dyadic model and proves energy dissipation occurs due to noise, challenging classical conservation expectations.

Findings

Energy dissipation occurs despite formal conservation laws.

Global regular solutions do not exist in the stochastic model.

Analysis of a birth-death process explains the dissipation mechanism.

Abstract

A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After some reductions, the main tool is the escape bahavior at infinity of a certain birth and death process.