Large Deviations for the Stochastic Shell Model of Turbulence

TL;DR

This paper establishes the existence, uniqueness, and large deviation principles for solutions to the stochastic GOY shell model of turbulence, advancing the mathematical understanding of turbulence modeling under randomness.

Contribution

It proves the strong solution's existence and uniqueness and derives a large deviation principle using the weak convergence approach for the stochastic GOY model.

Findings

Existence and uniqueness of strong solutions

Laplace principle established for the model

Large deviation principle derived using Wentzell-Freidellin approach

Abstract

In this work we first prove the existence and uniqueness of a strong solution to stochastic GOY model of turbulence with a small multiplicative noise. Then using the weak convergence approach, Laplace principle for so- lutions of the stochastic GOY model is established in certain Polish space. Thus a Wentzell-Freidlin type large deviation principle is established utilizing certain results by Varadhan and Bryc.