微极流体方程组零角度和黏性极限的边界效应
朱秀丽*,李华鹏,徐中海

(东北电力大学理学院,吉林 吉林 132012)

边界层; 边界层厚度; 收敛率

The Boundary Effects for the Micropolar Fluid Equations with Zero Limits of Angular and Micro-rotational Viscosities
ZHU Xiuli*,LI Huapeng,XU Zhonghai

(College of Science,Northeast Dianli University,Jilin 132012,China)

DOI: 10.6043/j.issn.0438-0479.201507018

备注

微极流体模型能够描述带有悬浮颗粒的黏性不可压流体的运动.考虑一类二位不可压缩微极流体方程组的初边值问题,证明了当角度和微旋转黏性(; ζ)趋于0时,方程组的解收敛于角度和微旋转黏性系数为零时方程的整体弱解.研究了微极流体方程组零角度和黏性极限的边界效应,给出了边界层厚度的阶数O(β)(0< β<2/3).与Chen等的结果相比,该边界层厚度更薄,并且提高了收敛率。

The micropolar fluid model can describe the motion of the viscous incompressible fluids with randomly oriented particles suspended in the medium.In this paper, we consider an initial-boundary value problem for two-dimensional incompressible micropolar fluid equations. Firstly, we prove that,as angular and micro-rotational viscosities(; ζ)approach zero,the solution converges to a global weak solution of the original equations with zero angular and micro-rotational viscosities. Secondly,we study the boundary layer effects. It is also shown that the boundary layer thickness is of the order O(β)with(0< β<2/3). In contrast with the result of Chen, the BL-thickness in the present analysis is thinner. In addition, the convergence rates are also improved.