Large deviation principle and inviscid shell models

TL;DR

This paper establishes a large deviation principle for inviscid shell models of turbulence with stochastic perturbations, analyzing the behavior as viscosity approaches zero and noise scales accordingly.

Contribution

It proves a large deviation principle for inviscid shell models with multiplicative noise, extending understanding of turbulence models under stochastic influences.

Findings

LDP holds for shell models with vanishing viscosity and scaled noise

The topology used is weaker than the natural one on V

The rate function is characterized via the inviscid equation solution

Abstract

A LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient converges to 0 and the noise intensity is multiplied by the square root of the viscosity, we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a H-valued Brownian motion satisfy a LDP in C([0,T],V) for the topology of uniform convergence on [0,T], but where V is endowed with a topology weaker than the natural one. The initial condition has to belong to V and the proof is based on the weak convergence of a family of stochastic control equations. The rate function is described in terms of the solution to the inviscid equation.