stochastic Leray-α model of Euler equations

We study the stochastic Leray-α model of Euler equations with transport noise. We first use weak convergence approach to show the large deviations of the stochastic Leray-α 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.