In this paper, we consider the pullback asymptotic behaviors of weak solutions for the 2D non-autonomous Non-Newtonian micropolar fluids. Employing the methods of ℓ-trajectories in [31], we first establish the existence of a finite dimensional pullback attractor and a pullback exponential attractor for the process ${\{L(t,\tau )\}}_{t\ge \tau }$ associated with (1.2)-(1.4) in the phase space $X_{\ell }$. Then we construct a pullback exponential attractor for the process ${\{U(t,\tau )\}}_{t\ge \tau }$ associated with (1.2)-(1.4) in the original phase space $H\times L^2(\mathrm{\Omega })$.

中文翻译：

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一类非牛顿微极性流体的回撤指数吸引子

在本文中，我们考虑了二维非自治非牛顿微极性流体的弱解的回拉渐近行为。采用的方法ℓ -trajectories在[31]，我们首先建立一个有限维拉回吸引子的过程的存在和拉回指数吸引${\{\mathrm{大号}（Ť，\tau ）\}}_{Ť\ge \tau }$ 与相空间中的（1.2）-（1.4）相关 $X_{\ell }$。然后我们为该过程构造一个回调指数吸引子${\{ü（Ť，\tau ）\}}_{Ť\ge \tau }$ 与原始相空间中的（1.2）-（1.4）相关 $H\times {\mathrm{大号}}^{\mathrm{2个}}（\mathrm{\Omega }）$。