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Local Well-Posedness for an IncompressibleEricksen-Leslie’s Liquid Crystals Model(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2020年04期
Page:
1-5
Research Field:
·数学·
Publishing date:

Info

Title:
Local Well-Posedness for an IncompressibleEricksen-Leslie’s Liquid Crystals Model
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)
Keywords:
liquid crystals; incompressible; local well-posedness
PACS:
O175.2
DOI:
10.3969/j.issn.1001-4616.2020.04.001
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.

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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Last Update: 2020-11-15