Communications in Mathematical Sciences

Volume 19 (2021)

Number 8

Approximations of the stochastic 3D Navier–Stokes equations with damping

Pages: 2249 – 2273



Hui Liu (School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, China)

Chengfeng Sun (School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, China)

Jie Xin (College of Information Science and Engineering, Shandong Agricultural University, Taian, Shandong, China)


The stochastic three-dimensional Navier–Stokes equation with damping is considered in this paper. We show that solutions of three-dimensional stochastic Navier–Stokes equation with damping driven by Brownian motion can be approximated by three-dimensional stochastic Navier–Stokes equation with damping driven by pure jump noise/random kicks on the spaces $D([0,T],V)$ and $D([0,T],H)$ for $3 \lt \beta \lt 5$ with any $\alpha \gt 0$ and $\alpha \geq \frac{1}{4}$ as $\beta=3$.


stochastic Navier–Stokes equation, approximations, weak convergence

2010 Mathematics Subject Classification

35Q30, 57Q55, 60H15, 76D05

The work is supported by the National Natural Science Foundation of China (Nos. 11901342, 11701269), the Natural Science Foundation of Shandong Province (No. ZR2018QA002), Postdoctoral Innovation Project of Shandong Province (No. 202003040) and China Postdoctoral Science Foundation (No. 2019M652350).

Received 13 January 2019

Accepted 19 May 2021

Published 7 October 2021