stochastic Leray-{\alpha} model of Euler equations

TL;DR

This paper investigates the stochastic Leray-α model of Euler equations with transport noise, analyzing large deviations, convergence rates, and a central limit theorem to understand its probabilistic behavior.

Contribution

It introduces a comprehensive analysis of the stochastic Leray-α Euler model, including large deviations, convergence rates, and a central limit theorem, which are novel in this context.

Findings

Large deviations established in a suitable scaling limit.

Quantitative convergence rates obtained via semigroup approach.

Central limit theorem with explicit convergence rate proved.

Abstract

We study the stochastic Leray-{\alpha} model of Euler equations with transport noise. We first use weak convergence approach to show the large deviations of the stochastic Leray-{\alpha} model of Euler equations in a suitable scaling limit. Then, we establish the quantitative convergence rate by semigroup approach. Moreover, we obtain a central limit theorem with strong convergence and get the explicit rate.