Stochastic inviscid shell models: well-posedness and anomalous dissipation

TL;DR

This paper investigates a stochastic inviscid shell model of turbulence, proving global solutions and energy dissipation despite the model's formal conservation laws, thus advancing understanding of turbulence dynamics.

Contribution

It introduces a stochastic version of a general inviscid shell model and establishes well-posedness and anomalous dissipation results.

Findings

Global weak existence and uniqueness of solutions

Energy dissipation occurs despite formal conservation

Applicable to models including GOY and Sabra shells

Abstract

In this paper we study a stochastic version of an inviscid shell model of turbulence with multiplicative noise. The deterministic counterpart of this model is quite general and includes inviscid GOY and Sabra shell models of turbulence. We prove global weak existence and uniqueness of solutions for any finite energy initial condition. Moreover energy dissipation of the system is proved in spite of its formal energy conservation.