Averaging principle for slow–fast stochastic 2D Navier–Stokes equation driven by Lévy noise

Abstract

This paper investigates the multiscale stochastic 2D Navier–Stokes equation driven by multiplicative Lévy noise. To be more precise, we establish the strong averaging principle for the stochastic 2D Navier–Stokes equation driven by Lévy noise, which involves a fast time scale component governed by a stochastic reaction‐diffusion equation driven by Lévy noise. The Khasminkii's time discretization approach and the technique of stopping time play the important roles in our proof.