柱对称可压缩液晶流体的剪切粘性极限

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 963-995.

柱对称可压缩液晶流体的剪切粘性极限

汤金良¹^,²(), 叶霞¹^,^*()

¹ 江西师范大学数学与统计学学院南昌 330022
² 深圳中学光明科学城学校广东深圳 518107

收稿日期:2025-03-24 修回日期:2026-01-19 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 叶霞 E-mail:sundaytjl@126.com;yexia@jxnu.edu.cn
作者简介:汤金良, E-mail:sundaytjl@126.com
基金资助:
国家自然科学基金(12461042);江西省学科学术和技术带头人培养项目-青年人才(20232BCJ23037);江西省自然科学基金(20232BAB211001);江西省自然科学基金(20242BAB25006)

The Limit of Vanishing Shear Viscosity for Compressible Nematic Liquid Crystal Flows with Cylindrical Symmetry

Jinliang Tang¹^,²(), Xia Ye¹^,^*()

¹ School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022
² 2Shenzhen High School Guangming Science City School, Guangdong Shenzhen 518107

Received:2025-03-24 Revised:2026-01-19 Online:2026-06-26 Published:2026-06-16
Contact: Xia Ye E-mail:sundaytjl@126.com;yexia@jxnu.edu.cn
Supported by:
NSFC(12461042);Jiangxi Province Key Subject Academic and Technical Leader Funding Project(20232BCJ23037);Natural Science Foundation of Jiangxi Province(20232BAB211001);Natural Science Foundation of Jiangxi Province(20242BAB25006)

摘要/Abstract

摘要：

该文主要考虑柱对称可压缩液晶流体的剪切粘性极限问题. 在初值无小性条件下, 作者证明了随着剪切粘性的消失, 解的收敛速度以及分析了边界层函数的性质.

关键词: 液晶流, 粘性极限, 最佳收敛速度, 边界层.

Abstract:

This paper is concerned with compressible nematic liquid crystal flows with cylindrical symmetry. We prove the rate of convergence as the limit of vanishing shear viscosity, and we also establish the properties of the boundary layer function. Our results do not require the smallness of the initial data.

Key words: nematic liquid crystal flow, vanishing shear viscosity, optimal convergence efficiency, boundary layer.

中图分类号:

O175.25

汤金良, 叶霞. 柱对称可压缩液晶流体的剪切粘性极限[J]. 数学物理学报, 2026, 46(3): 963-995.

Jinliang Tang, Xia Ye. The Limit of Vanishing Shear Viscosity for Compressible Nematic Liquid Crystal Flows with Cylindrical Symmetry[J]. Acta mathematica scientia,Series A, 2026, 46(3): 963-995.

参考文献 23

[1]	Ding S J, Wang C Y, Wen H Y. Weak solution to compressible hydrodynamic flow of liquid crystals in dimension one. Discrete Contin Dyn Syst Ser B, 2011, 15 : 357-371 doi: 10.3934/dcdsb.2011.15.357
[2]	Ding S J, Lin J Y, Wang C Y, Wen H Y. Compressible hydrodynamic flow of liquid crystals in 1-D. Discrete Contin Dyn Syst, 2012, 32 : 539-563 doi: 10.3934/dcds.2012.32.539
[3]	Ericksen J. Conservation laws for liquid crystals. Trans Soc Rheol, 1961, 5 : 23-34
[4]	Frid H, Shelukhin V V. Vanishing shear viscosity in the equations of compressible fluids for the flows with the cylinder symmetry. SIAM J Math Anal, 2000, 31 : 1144-1156 doi: 10.1137/S003614109834394X
[5]	Hu X, Wu G. Global solution to the three-dimensional compressible flow of liquid crystals. SIAM J Math Anal, 2013, 45 (5): 2678-2699 doi: 10.1137/120898814
[6]	Huang T, Wang C, Wen H. Strong solutions of the compressible nematic liquid crystal flow. J Diff Eqs, 2012, 252 : 2222-2256 doi: 10.1016/j.jde.2011.07.036
[7]	Huang T, Wang C Y, Wen H Y. Blow up criterion for compressible nematic liquid crystal flows in dimension three. Arch Rat Mech Anal, 2012, 204 (1): 285-311 doi: 10.1007/s00205-011-0476-1
[8]	Jiang F, Jiang S, Wang D. On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a bounded domain. J Funct Anal, 2013, 265 (12): 3369-3397 doi: 10.1016/j.jfa.2013.07.026
[9]	Jiang S, Zhang J W. Boundary layers for the Navier-Stokes equations of compressible heat-conducting flows with cylindrical symmetry. SIAM J Math Anal, 2009, 41 : 237-268 doi: 10.1137/07070005X
[10]	Li J, Xu Z, Zhang J. Global existence of classical solutions with large oscillations and vacuum to the three-dimensional compressible nematic liquid crystal flows. J Math Fluid Mech, 2018, 20 (4): 2105-2145 doi: 10.1007/s00021-018-0400-7
[11]	Lin J, Lai B, Wang C. Global finite energy weak solutions to the compressible nematic liquid crystal flow in dimension three. SIAM J Math Anal, 2015, 47 (4): 2952-2983 doi: 10.1137/15M1007665
[12]	Liu Y. On the global existence of classical solutions for compressible nematic liquid crystal flows with vacuum. Z Angew Math Phys, 2020, 71 (1): 1-16 doi: 10.1007/s00033-019-1224-x
[13]	Liu Y, Zhong X. Global existence of strong solutions with large oscillations and vacuum to the compressible nematic liquid crystal flows in 3D bounded domains. arXiv:2204.06227
[14]	Qin X L, Yang T, Yao Z A, Zhou W S. Vanishing shear viscosity and boundary layer for the Navier-Stokes equations with cylindrical symmetry. Arch Ration Mech Anal, 2015, 216 (3): 1049-1086 doi: 10.1007/s00205-014-0826-x
[15]	Sun Y, Zhong X. Global strong solutions to the compressible nematic liquid crystal flows with large oscillations and vacuum in 2D bounded domains. J Geom Anal, 2023, 33 (10): Art 319
[16]	Tao Q, Gao J, Yao Z. Global strong solutions of the compressible nematic liquid crystal flow with the cylinder symmetry. Commun Math Sci, 2015, 13 (8): 2065-2096 doi: 10.4310/CMS.2015.v13.n8.a5
[17]	Wang Y H, Wen H Y, Zhang W H. Vanishing shear viscosity limit for the Navier-Stokes equations with cylindrical symmetry: boundary layer and optimal convergence rate. SIAM J Math Anal, 2023, 55 (3): 1631-1675 doi: 10.1137/22M1509321
[18]	Wang D, Yu C. Global weak solution and large-time behavior for the compressible flow of liquid crystals. Arch Ration Mech Anal, 2012, 204 (3): 881-915 doi: 10.1007/s00205-011-0488-x
[19]	Wang F, Zhong X. Global well-posedness to the compressible nematic liquid crystal flows with large oscillations and vacuum in 3D exterior domains. J Math Phys, 2023, 64 (2): Art 021505
[20]	Wen H, Yang T, Zhao X, Zhu C. Optimal convergence rate of the vanishing shear viscosity limit for compressible Navier-Stokes equations with cylindrical symmetry. J Math Pures Appl, 2021, 146 (9): 99-126 doi: 10.1016/j.matpur.2020.09.003
[21]	Wu G, Tan Z. Global low-energy weak solution and large-time behavior for the compressible flow of liquid crystals. J Diff Eqs, 2018, 264 (11): 6603-6632 doi: 10.1016/j.jde.2018.01.045
[22]	Yao L, Zhang T, Zhu C J. Boundary layers for compressible Navier-Stokes equations with density dependent viscosity and cylindrical symmetry. Ann Inst H Poincar Anal NonLinaire, 2011, 28 : 677-709
[23]	Ye X, Zhang J W. Boundary-layer phenomena for the cylindrically symmetric Navier-Stokes equations of compressible heat-conducting fluids with large data at vanishing shear viscosity. Nonlinearity, 2016, 29 (8): 2395-2416 doi: 10.1088/0951-7715/29/8/2395