Bulletin of the Malaysian Mathematical Sciences Society ( IF 1.0 ) Pub Date : 2021-05-17 , DOI: 10.1007/s40840-021-01138-3 Yana Guo , Yan Jia , Bo-Qing Dong
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.
中文翻译:
角粘度为零的微极性方程的时间衰减率
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。