Averaging principle for slow–fast stochastic 2D Navier–Stokes equation driven by Lévy noise. (26th December 2020)

• Record Type: Journal Article
• Authors: Gao, Junrong; Li, Shihu; Sun, Xiaobin; Xie, Yingchao
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 7(2021)
• Page Start: 5475
• Page End: 5500
• Publication Date: 2020-12-26
• Subjects: averaging principle -- Lévy noise -- multiscale -- stochastic 2D Navier–Stokes equation -- strong convergence; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7123
• Languages: English
• ISSNs: 0170-4214

Abstract

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.