Anomalous dissipation in a stochastic inviscid dyadic model

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.

Published in at http://dx.doi.org/10.1214/11-AAP768 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture
• Simple Systems with Anomalous Dissipation and Energy Cascade
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Cited by in corpus (8)

• Stochastic Navier-Stokes Equations and Related Models
• On a Stochastic Leray-α model of Euler equations
• Uniqueness for an inviscid stochastic dyadic model on a tree
• Well posedness and limit theorems for a class of stochastic dyadic models
• Dyadic models for fluid equations: a survey
• Stochastic inviscid shell models: well-posedness and anomalous dissipation
• Dyadic models for ideal MHD
• Linear Stochastic Dyadic model