The uniform asymptotic behavior of solutions for 2D g-Navier-Stokes equations with nonlinear dampness and its dimensions

Xiaoxia Wang; Jinping Jiang; Xiaoxia Wang; Jinping Jiang

doi:10.3934/era.2023201

Electronic Research Archive

2023, Volume 31, Issue 7: 3963-3979. doi: 10.3934/era.2023201

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Research article

The uniform asymptotic behavior of solutions for 2D g-Navier-Stokes equations with nonlinear dampness and its dimensions

Xiaoxia Wang ^,,
Jinping Jiang

College of Mathematics and Computer Science, Yan'an University, Yan'an 716000, China

Received: 14 January 2023 Revised: 13 April 2023 Accepted: 21 April 2023 Published: 16 May 2023

In this paper, the uniform asymptotic behavior of solutions for 2D g-Navier-Stokes equations with nonlinear dampness is studied in unbounded domain. The uniform asymptotic properties of the process family is proved with the energy equation method and the uniform attractor is obtained. Finally, the dimension of the uniform attractor is estimated in the quasi-periodical case.
- g-Navier-Stokes equations,
- energy equation method,
- nonlinear dampness,
- global well-posedness,
- dimensional estimation
Citation: Xiaoxia Wang, Jinping Jiang. The uniform asymptotic behavior of solutions for 2D g-Navier-Stokes equations with nonlinear dampness and its dimensions[J]. Electronic Research Archive, 2023, 31(7): 3963-3979. doi: 10.3934/era.2023201

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Abstract

In this paper, the uniform asymptotic behavior of solutions for 2D g-Navier-Stokes equations with nonlinear dampness is studied in unbounded domain. The uniform asymptotic properties of the process family is proved with the energy equation method and the uniform attractor is obtained. Finally, the dimension of the uniform attractor is estimated in the quasi-periodical case.

References

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