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Research Article | Open Access

Determination of the 3D Navier-Stokes equations with damping

Wei Shi1, Xinguang Yang1( ), Xingjie Yan2
Department of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China
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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.

Keywords

determinationNavier-Stokes equationdamping

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Electronic Research Archive
Volume 30 Issue 10,
October 2022
Pages 3872-3886
DOI: 10.3934/era.2022197

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Cite this article:
Shi W, Yang X, Yan X. Determination of the 3D Navier-Stokes equations with damping. Electronic Research Archive, 2022, 30(10): 3872-3886. https://doi.org/10.3934/era.2022197

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Received: 14 July 2022
Revised: 15 August 2022
Accepted: 21 August 2022
Published: 15 October 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)