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Research Article | Open Access

Stability for a 3D Ladyzhenskaya fluid model with unbounded variable delay

Pan Zhang, Lan Huang( )
College of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
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Abstract

This paper is concerned with the stability of solutions to a Ladyzhenskaya fluid model with unbounded variable delay. We first prove the existence, uniqueness and regularity of global weak solutions to the Ladyzhenskaya model by using Galerkin approximations and the energy method based on some suitable assumptions about external forces. Then we obtain that the stationary solution is locally stable. Finally, we establish that the stationary solution has polynomial stability in a particular case of unbounded variable delay.

Keywords

Ladyzhenskaya modelunbounded variable delaysasymptotic stability

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Electronic Research Archive
Volume 31 Issue 12,
December 2023
Pages 7602-7627
DOI: 10.3934/era.2023384

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Cite this article:
Zhang P, Huang L. Stability for a 3D Ladyzhenskaya fluid model with unbounded variable delay. Electronic Research Archive, 2023, 31(12): 7602-7627. https://doi.org/10.3934/era.2023384

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Received: 26 September 2023
Revised: 13 November 2023
Accepted: 22 November 2023
Published: 15 December 2023
©2023 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)