数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 2108-2120.doi: 10.1007/s10473-023-0511-y

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DYNAMICS OF THE STOCHASTIC $g$-NAVIER-STOKES EQUATIONS DRIVEN BY NONLINEAR NOISE*

Tao Yan, Lu Zhang, Aihong Zou, Ji Shu   

  1. School of Mathematical Sciences, Laurent Mathematics Center and V. C. & V. R. Key Lab, Sichuan Normal University, Chengdu 610066, China
  • 收稿日期:2021-11-16 修回日期:2023-04-20 出版日期:2023-10-26 发布日期:2023-10-25

DYNAMICS OF THE STOCHASTIC $g$-NAVIER-STOKES EQUATIONS DRIVEN BY NONLINEAR NOISE*

Tao Yan, Lu Zhang, Aihong Zou, Ji Shu   

  1. School of Mathematical Sciences, Laurent Mathematics Center and V. C. & V. R. Key Lab, Sichuan Normal University, Chengdu 610066, China
  • Received:2021-11-16 Revised:2023-04-20 Online:2023-10-26 Published:2023-10-25
  • Contact: †Ji Shu, E-mail: shuji@sicnu.edu.cn
  • About author:Tao Yan, E-mail: 303809632@qq.com; Lu Zhang, E-mail: 786614079@qq.com; Aihong Zou, E-mail: 1760152877@qq.com
  • Supported by:
    Shu’s research was supported by the National Natural Science Foundation of China (11871138) and the Sichuan Science and Technology Program (2023NSFSC0076).

摘要: This paper deals with the asymptotic behavior of solutions of the stochastic $g$-Navier-Stokes equation driven by nonlinear noise. The existence and uniqueness of weak pullback mean random attractors for the equation in Bochner space is proven for when the diffusion terms are Lipschitz nonlinear functions. Furthermore, we also establish the existence of invariant measures for the equation.

关键词: non-Newtonian fluid, weak pullback attractor, mean random dynamical system, nonlinear noise, invariant measure

Abstract: This paper deals with the asymptotic behavior of solutions of the stochastic $g$-Navier-Stokes equation driven by nonlinear noise. The existence and uniqueness of weak pullback mean random attractors for the equation in Bochner space is proven for when the diffusion terms are Lipschitz nonlinear functions. Furthermore, we also establish the existence of invariant measures for the equation.

Key words: non-Newtonian fluid, weak pullback attractor, mean random dynamical system, nonlinear noise, invariant measure

中图分类号: 

  • 37L55