# Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations

## TL;DR

This paper demonstrates that, under specific noise scaling, solutions of stochastic 2D Euler equations converge to deterministic 2D Navier-Stokes solutions, revealing insights into their approximate uniqueness and mixing properties.

## Contribution

It establishes a scaling limit where stochastic 2D Euler equations converge to deterministic Navier-Stokes equations, linking stochastic and deterministic fluid dynamics.

## Key findings

- Solutions converge weakly to Navier-Stokes equations under noise scaling
- Weak solutions exhibit approximate uniqueness
- Solutions demonstrate weakly quenched exponential mixing

## Abstract

We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with transport type noises and $L^2$-initial data. Under a suitable scaling of the noises, we show that the solutions converge weakly to that of the deterministic 2D Navier--Stokes equations. Consequently, we deduce that the weak solutions of the stochastic 2D Euler equations are approximately unique and "weakly quenched exponential mixing".