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.”

中文翻译：

---

具有运输噪声的随机二维Euler方程的标度极限到确定性Navier–Stokes方程

我们考虑了圆环上具有涡度形式的一类随机二维Euler方程，具有运输类型的噪声和\（L ^ 2 \）初始数据。在适当缩放噪声的条件下，我们证明了解决方案与确定性二维Navier–Stokes方程的收敛性较弱。因此，我们推论出随机二维Euler方程的弱解是近似唯一的，并且“弱淬灭指数混合”。