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

Pan Zhang; Lan Huang; Pan Zhang; Lan Huang

doi:10.3934/era.2023384

Electronic Research Archive

2023, Volume 31, Issue 12: 7602-7627. doi: 10.3934/era.2023384

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Research article

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

Received: 26 September 2023 Revised: 13 November 2023 Accepted: 22 November 2023 Published: 05 December 2023

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.
- Ladyzhenskaya model,
- unbounded variable delays,
- asymptotic stability
Citation: Pan Zhang, Lan Huang. Stability for a 3D Ladyzhenskaya fluid model with unbounded variable delay[J]. Electronic Research Archive, 2023, 31(12): 7602-7627. doi: 10.3934/era.2023384

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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.

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