Determination of the 3D Navier-Stokes equations with damping

Wei Shi; Xinguang Yang; Xingjie Yan; Wei Shi; Xinguang Yang; Xingjie Yan

doi:10.3934/era.2022197

Electronic Research Archive

2022, Volume 30, Issue 10: 3872-3886. doi: 10.3934/era.2022197

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Determination of the 3D Navier-Stokes equations with damping

1.
Department of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2.
Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China

Academic Editor: Baowei Feng

Received: 14 July 2022 Revised: 15 August 2022 Accepted: 21 August 2022 Published: 25 August 2022

This paper is concerned the determination of trajectories for the three-dimensional Navier-Stokes equations with nonlinear damping subject to periodic boundary condition. By using the energy estimate of Galerkin approximated equation, the finite number of determining modes and asymptotic determined functionals have been shown via the Grashof numbers for the non-autonomous and autonomous damped Navier-Stokes fluid flow respectively.
- determination,
- Navier-Stokes equation,
- damping
Citation: Wei Shi, Xinguang Yang, Xingjie Yan. Determination of the 3D Navier-Stokes equations with damping[J]. Electronic Research Archive, 2022, 30(10): 3872-3886. doi: 10.3934/era.2022197

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Abstract

This paper is concerned the determination of trajectories for the three-dimensional Navier-Stokes equations with nonlinear damping subject to periodic boundary condition. By using the energy estimate of Galerkin approximated equation, the finite number of determining modes and asymptotic determined functionals have been shown via the Grashof numbers for the non-autonomous and autonomous damped Navier-Stokes fluid flow respectively.

References

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