[1]牛 聪,孙建筑,唐 童.不可压缩Ericksen-Leslie液晶模型局部适定性的研究[J].南京师大学报(自然科学版),2020,43(04):1-5.[doi:10.3969/j.issn.1001-4616.2020.04.001]
　Niu Cong,Sun Jianzhu,Tang Tong.Local Well-Posedness for an IncompressibleEricksen-Leslie’s Liquid Crystals Model[J].Journal of Nanjing Normal University(Natural Science Edition),2020,43(04):1-5.[doi:10.3969/j.issn.1001-4616.2020.04.001]
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不可压缩Ericksen-Leslie液晶模型局部适定性的研究()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第43卷
期数:
2020年04期
页码:
1-5
栏目:
·数学·
出版日期:
2020-12-30

文章信息/Info

Title:
Local Well-Posedness for an IncompressibleEricksen-Leslie’s Liquid Crystals Model
文章编号:
1001-4616(2020)04-0001-05
作者:
牛 聪1; 孙建筑2; 唐 童1
(1.河海大学理学院,江苏 南京 210098)(2.南京林业大学应用数学系,江苏 南京 210037)
Author(s):
Niu Cong1; Sun Jianzhu2; Tang Tong1
(1.College of Science,Hohai University,Nanjing 210098,China)(2.Department of Applied Mathematics,Nanjing Forestry University,Nanjing 210037,China)
关键词:
液晶; 不可压缩; 局部适定性
Keywords:
liquid crystals; incompressible; local well-posedness
分类号:
O175.2
DOI:
10.3969/j.issn.1001-4616.2020.04.001
文献标志码:
A
摘要:
本文证明了不可压缩Ericksen-Leslie系统的抛物双曲真空液晶模型强解的局部适定性.
Abstract:
In this paper,we prove local well-posedness of strong solutions to an incompressible Ericksen-Leslie’s parabolic-hyperbolic liquid crystals model with vacuum.

参考文献/References:

[1] ERICKSEN J L. Conservation laws for liquid crystals[J]. Transactions of the society of rheology,1961,5:23-34.
[2]ERICKSEN J L. Hydrostatic theory of liquid crystals[J]. Archive for rational mechanics and analysis,1962,9:371-378.
[3]ERICKSEN J L. Liquid crystals with variable degree of orientation[J]. Archive for rational mechanics and analysis,1990,113(2):97-120.
[4]LESLIE F. Some constitutive equations for liquid crystals[J]. Archive for rational mechanics and analysis,1968,28(4):265-283.
[5]HUANG T,WANG C Y,WEN H Y. Strong solutions of the compressible nematic liquid crystal flow[J]. Journal of differential equations,2012,252(3):2222-2265.
[6]DING S J,HUANG J R,WEN H Y,et al. Incompressible limit of the compressible nematic liquid crystal flow[J]. Journal of functional analysis,2013,264(7):1711-1756.
[7]HUANG T,WANG C Y,WEN H Y. Blow up criterion for compressible nematic liquid crystal flows in dimension three[J]. Archive for rational mechanics and analysis,2012,204(1):285-311.
[8]FAN J S,LI F C,NAKAMURA G. Local well-posedness for a compressible non-isothermal model for nematic liquid crystals[J]. Journal of mathematical physics,2018,59(3):031503.
[9]刘兰明. 液晶动力学方程数学研究[D]. 上海:复旦大学,2012.
[10]FAN J S,ZHOU Y. Uniform local well-posedness for an Ericksen-Leslie’s density-dependent parabolic-hyperbolic liquid crystals model[J]. Applied mathematics letters,2017,74:79-84.
[11]FAN J S,SAMET B,ZHOU Y. A regularity criterion for a density-dependent incompressible liquid crystals model with vacuum[J]. Hiroshima mathematical journal,2019,49(1):129-138.
[12]FAN J S,ZHOU Y. A regularity criterion for a 3D density-dependent incompressible liquid crystals model[J]. Applied mathematics letters,2016,58:119-124.
[13]WEN H Y,DING S J. Solutions of incompressible hydrodynamic flow of liquid crystals[J]. Nonlinear analysis real world applications,2011,12(3):1510-1531.
[14]JIANG N,LUO Y L. On well-posedness of Ericksen-Leslie’s hyperbolic incompressible liquid crystal model[J]. SIAM journal on mathematical analysis,2019,51(1):403-434.
[15]王伟. 液晶动力学方程的理论分析[D]. 北京:北京大学,2012.
[16]LU S Q,CHEN M C,LIU Q L. On regularity for an Ericksen-Leslie’s parabolic-hyperbolic liquid crystals model[J]. Zeitschrift für angewandte mathematik und mechanik,2018,98(9):1574-1584.
[17]METIVIER G,SCHOCHET S. The incompressible limit of the non-isentropic Euler equations[J]. Archive for rational mechanics and analysis,2001,158(1):61-90.
[18]ALAZARD T. Low Mach number limit of the full Navier-Stokes equations[J]. Archive for rational mechanics and analysis,2006,180(1):1-73.
[19]DOU C S,JIANG S,OU Y B. Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain[J]. Journal of differential equations,2015,258(2):379-398.
[20]KATO T,PONCE G. Commutator estimates and the Euler and Navier-Stokes equations[J]. Communications on pure and applied mathematics,1988,41(7):891-907.

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备注/Memo

备注/Memo:
收稿日期:2019-09-26.
基金项目:国家自然科学基金项目(11801138).
通讯作者:唐童,副教授,研究方向:偏微分方程. E-mail:tt0507010156@126.com
更新日期/Last Update: 2020-11-15