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

Abstract

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.

Keywords

• Micropolar fluid flow
• pullback attractor
• truncation function
• tempered behavior
• upper semicontinuity