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

Abstract

<abstract><p>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. $</p></abstract>