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[1]朱秀丽*,李华鹏,徐中海.微极流体方程组零角度和黏性极限的边界效应[J].厦门大学学报(自然科学版),2017,56(01):97-101.[doi:10.6043/j.issn.0438-0479.201507018]
 ZHU Xiuli*,LI Huapeng,XU Zhonghai.The Boundary Effects for the Micropolar Fluid Equations with Zero Limits of Angular and Micro-rotational Viscosities[J].Journal of Xiamen University(Natural Science),2017,56(01):97-101.[doi:10.6043/j.issn.0438-0479.201507018]
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微极流体方程组零角度和黏性极限的边界效应(PDF)
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
56卷
期数:
2017年01期
页码:
97-101
栏目:
研究论文
出版日期:
2017-01-23

文章信息/Info

Title:
The Boundary Effects for the Micropolar Fluid Equations with Zero Limits of Angular and Micro-rotational Viscosities
文章编号:
0438-0479(2017)01-0097-05
作者:
朱秀丽*李华鹏徐中海
东北电力大学理学院,吉林 吉林 132012
Author(s):
ZHU Xiuli*LI HuapengXU Zhonghai
College of Science,Northeast Dianli University,Jilin 132012,China
关键词:
边界层 边界层厚度 收敛率
Keywords:
boundary layer boundary layer-thickness convergence rates
分类号:
O 175.2
DOI:
10.6043/j.issn.0438-0479.201507018
文献标志码:
A
摘要:
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。
Abstract:
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.

参考文献/References:

[1] CHEN M T,XU X Y,ZHANG J W.The zero limits of angular and micro-rotational viscosities for the two-dimensional micropolar fluid equations with boundary effects[J].Z Angew Math Phys,2014,65:687-710.
[2] 刘生全,徐忠海.黏性系数依赖于密度的一维黏性Navier-Stokcs方程组解的全局存在性[J].东北电力大学学报,2014,34(2):87-91.
[3] 张大鹏,薛雯,朱秀丽,等.一类二阶常微分方程初值问题解的性质的完全证明[J].东北电力大学学报,2016,36(4):96-98.
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[5] XUE L.Well-posedness and zero micro-rotation viscosity limit of the 2D micropolar fluid equations[J].Math Meth Appl Sci,2011,34:1760-1777.
[6] DONG B,ZHANG Z.Global regularity of the 2D micropolar fluid flows with zero angular viscosity[J].J Diff Eqns,2010,249:200-213.
[7] YAMAGUCHI N.Existence of global strong solution to the micropolar fluid system in a bounded domain[J].Math Meth Appl Sci,2005,28:1507-1506.
[8] JIANG S,ZHANG J W,ZHAO J N.Boundary-layer effects for the 2-D Boussinesq equations with vanishing diffusivity limit in the half plane[J].J Diff Eqns,2011,250:3907-3936.
[9] YAO L,ZHANG T,ZHU C J.Boundary layers for compressible Navier-Stokes equations with density-dependent viscosity and cylindrical symmetry[J].Ann Inst H Poincaré Anal Non Linéaire,2011,28:677-709.
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备注/Memo

备注/Memo:
收稿日期:2016-01-08 录用日期:2016-12-22
基金项目:国家自然科学基金(11271153); 高等学校博士学科点专项科研基金(20140101-20161231); 吉林省科技发展计划项目(20150101002JC); 吉林省教育厅“十三五”科学技术研究项目(吉教科合字[2016]第81号); 东北电力大学博士科研启动基金(BSJXM-201331)
*通信作者:zhuxiulijl@163.com
更新日期/Last Update: 1900-01-01