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

doi:10.1007/s10473-023-0511-y

Acta mathematica scientia,Series A ›› 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^†

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).

Abstract

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

CLC Number:

37L55

Tao Yan, Lu Zhang, Aihong Zou, Ji Shu. DYNAMICS OF THE STOCHASTIC $g$-NAVIER-STOKES EQUATIONS DRIVEN BY NONLINEAR NOISE^*[J].Acta mathematica scientia,Series A, 2023, 43(5): 2108-2120.

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

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