2D Euler equations with Stratonovich transport noise as a large scale stochastic model reduction

TL;DR

This paper investigates the stochastic reduction of 2D Euler equations with Stratonovich transport noise, demonstrating convergence results that simplify complex fluid-dynamics models with multiple time scales.

Contribution

It provides the first rigorous analysis of the limit from an Euler-type system to stochastic 2D Euler equations with transport noise, establishing convergence results.

Findings

Weak convergence of vorticity field

Strong convergence of velocity field

Stochastic model reduction for multi-scale fluid dynamics

Abstract

The limit from an Euler type system to the 2D Euler equations with Stratonovich transport noise is investigated. A weak convergence result for the vorticity field and a strong convergence result for the velocity field are proved. Our results aim to provide a stochastic reduction of fluid-dynamics models with three different time scales.