The boundedness of pullback attractors for delayed non-Newtonian fluids

Tingting Liao; Guowei Liu; Tianfang Wu; Tingting Liao; Guowei Liu; Tianfang Wu

doi:10.3934/cam.2026025

Communications in Analysis and Mechanics

2026, Volume 18, Issue 3: 610-625. doi: 10.3934/cam.2026025

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Research article

The boundedness of pullback attractors for delayed non-Newtonian fluids

1.
School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China
2.
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China
3.
Wenzhou Businesss College, Wenzhou, 325035, China

Received: 07 September 2025 Revised: 24 March 2026 Accepted: 06 May 2026 Published: 03 August 2026
35B41, 35B65, 35Q30

We investigated the boundedness of pullback attractors for non-Newtonian fluids with delay in two-dimensional bounded domains. Under suitable assumptions on the delay term, we established the boundedness of the pullback attractor, defined in the phase space $ \mathbb{L}^2 $, which was bounded in $ \mathbb{H}^4 $ by means of refined energy estimates.
- boundedness,
- non-Newtonian fluid,
- pullback attractor
Citation: Tingting Liao, Guowei Liu, Tianfang Wu. The boundedness of pullback attractors for delayed non-Newtonian fluids[J]. Communications in Analysis and Mechanics, 2026, 18(3): 610-625. doi: 10.3934/cam.2026025

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Abstract

We investigated the boundedness of pullback attractors for non-Newtonian fluids with delay in two-dimensional bounded domains. Under suitable assumptions on the delay term, we established the boundedness of the pullback attractor, defined in the phase space $ \mathbb{L}^2 $, which was bounded in $ \mathbb{H}^4 $ by means of refined energy estimates.

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