This paper is concerned with the large time decay rates of the two-dimensional (2D) micropolar equations with zero angular viscosity. Based on the generalized Fourier splitting methods and low frequency effect analysis, we firstly obtain the solutions decay as \(\Vert u\Vert _{L^2}+ \Vert \omega \Vert _{L^2}\le C(1+t)^{-\frac{1}{2}}\). Moreover, by exploring the new structure of the system, we obtain a new improved decay rates \(\Vert \omega \Vert _{L^2}+ \Vert \nabla u\Vert _{L^2}\le C(1+t)^{-1}\). Our methods here are also available to the time decay issue of the complex fluid flows with partial dissipation.

本文关注的是零黏度为零的二维（2D）微极性方程的大时间衰减率。基于广义傅里叶分裂方法和低频效果分析，我们首先获得解衰减为\（\ Vert u \ Vert _ {L ^ 2} + \ Vert \ omega \ Vert _ {L ^ 2} \ le C（ 1 + t）^ {-\ frac {1} {2}} \）。此外，通过探索系统的新结构，我们获得了新的改进的衰减率\（\ Vert \ omega \ Vert _ {L ^ 2} + \ Vert \ nabla u \ Vert _ {L ^ 2} \ le C（ 1 + t）^ {-1} \）。我们的方法也可用于部分耗散的复杂流体流的时间衰减问题。