Electronic Journal of Differential Equations (Jan 2018)

Asymptotic behavior of pullback attractors for non-autonomous micropolar fluid flows in 2D unbounded domains

  • Wenlong Sun,
  • Yeping Li

Journal volume & issue
Vol. 2018, no. 03,
pp. 1 – 21

Abstract

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In this article, we investigate the pullback asymptotic behavior of solutions for a non-autonomous micropolar fluid flows in 2D unbounded channel-like domains. First, applying the technique of truncation functions, decomposition of spatial domain, and the energy method, we show the existence of the pullback attractor in the space $\widehat{H}(\Omega)$ (has L^2-regularity). In fact, we can deduce the existence of pullback attractor in space $\widehat{V}(\Omega)$ (has H^1-regularity). Also the tempered behavior of the pullback attractor is verified. Moreover, when the spatial domain varies from $\Omega_m$ ($\{\Omega_m\}_{m=1}^{\infty}$ be an expanding sequence of simply connected, bounded and smooth subdomains of $\Omega$ such that $\cup_{m=1}^{\infty}\Omega_m = \Omega$) to $\Omega$, the upper semicontinuity of the pullback attractor is discussed.

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