In this paper, we consider the long-time behavior of weak solutions for the 2D autonomous non-Newtonian micropolar fluids. By means of the method of ℓ-trajectories introduced by Málek and Pražák, we first establish the existence of global attractor for solution semigroup {S(t)}_t ≥ 0 associated with (1)–(3) and estimate the fractal dimension of global attractor in H × L²(Ω) is finite. Then we derive the existence of exponential attractor for solution semigroup {S(t)}_t ≥ 0 associated with (1.1)-(1.3) in H × L²(Ω).

中文翻译：

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一类非牛顿微极流体的全局和指数吸引子

在本文中，我们考虑了二维自主非牛顿微极流体弱解的长期行为。通过的方法的手段ℓ -trajectories通过马利克和Pražák引入，我们首先建立全球吸引子的存在为溶液半群{小号（吨）}_吨 ≥0与（1）相关联的- （3）和估计的分形维数H  ×  L ² (Ω) 中的全局吸引子是有限的。然后我们推导出对于解半群 { S ( t )} _{t  ≥ 0}与 (1.1)-(1.3) 在H  ×  L ^{2 中}存在指数吸引子(Ω)。