Upper semi-continuity of pullback attractors for bipolar fluids with delay

Guowei Liu; Hao Xu; Caidi Zhao; Guowei Liu; Hao Xu; Caidi Zhao

doi:10.3934/era.2023305

Electronic Research Archive

2023, Volume 31, Issue 10: 5996-6011. doi: 10.3934/era.2023305

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Research article

Upper semi-continuity of pullback attractors for bipolar fluids with delay

1.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China
2.
Department of Mathematics, Wenzhou University, Wenzhou 325035, China

Received: 27 February 2023 Revised: 17 July 2023 Accepted: 03 August 2023 Published: 05 September 2023

We investigate bipolar fluids with delay in a $ 2D $ channel $ \Sigma = \mathbb{R}\times (-K, K) $ for some $ K > 0 $. The channel $ \Sigma $ is divided into a sequence of simply connected, bounded, and smooth sub-domains $ \Sigma_n (n = 1, 2, 3\cdot\cdot\cdot) $, such that $ \Sigma_n\rightarrow \Sigma $ as $ n\rightarrow \infty $. The paper demonstrates that the pullback attractors in the sub-domains $ \Sigma_n $ converge to the pullback attractor in the entire domain $ \Sigma $ as $ n\rightarrow \infty. $
- bipolar fluid,
- delay,
- pullback attractor,
- upper semi-continuity
Citation: Guowei Liu, Hao Xu, Caidi Zhao. Upper semi-continuity of pullback attractors for bipolar fluids with delay[J]. Electronic Research Archive, 2023, 31(10): 5996-6011. doi: 10.3934/era.2023305

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Abstract

We investigate bipolar fluids with delay in a $ 2D $ channel $ \Sigma = \mathbb{R}\times (-K, K) $ for some $ K > 0 $. The channel $ \Sigma $ is divided into a sequence of simply connected, bounded, and smooth sub-domains $ \Sigma_n (n = 1, 2, 3\cdot\cdot\cdot) $, such that $ \Sigma_n\rightarrow \Sigma $ as $ n\rightarrow \infty $. The paper demonstrates that the pullback attractors in the sub-domains $ \Sigma_n $ converge to the pullback attractor in the entire domain $ \Sigma $ as $ n\rightarrow \infty. $

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