Well-posedness and long term behavior of a simplified Ericksen-Leslie non-autonomous system for nematic liquid crystal flows

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2012.11.407 ◽

2012 ◽

Vol 11 (2) ◽

pp. 407-441 ◽

Author(s):

Stefano Bosia ◽

Keyword(s):

Liquid Crystal ◽

Nematic Liquid Crystal ◽

Autonomous System ◽

Well Posedness ◽

Nematic Liquid Crystal Flows ◽

Long Term Behavior

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Global well-posedness of the 2D nonhomogeneous incompressible nematic liquid crystal flows

Journal of Differential Equations ◽

10.1016/j.jde.2016.08.044 ◽

2016 ◽

Vol 261 (11) ◽

pp. 6521-6569 ◽

Author(s):

Qiao Liu ◽

Shengquan Liu ◽

Wenke Tan ◽

Xin Zhong

Keyword(s):

Liquid Crystal ◽

Nematic Liquid Crystal ◽

Well Posedness ◽

Nematic Liquid Crystal Flows

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Global well‐posedness of the 3D incompressible nematic liquid crystal flows with density‐dependent viscosity coefficient

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.6341 ◽

2020 ◽

Vol 43 (9) ◽

pp. 5985-6010

Author(s):

Yang Liu

Keyword(s):

Liquid Crystal ◽

Nematic Liquid Crystal ◽

Viscosity Coefficient ◽

Well Posedness ◽

Density Dependent ◽

Nematic Liquid Crystal Flows ◽

Dependent Viscosity

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Uniform well-posedness and low Mach number limit to the compressible nematic liquid crystal flows in a bounded domain

Nonlinear Analysis ◽

10.1016/j.na.2015.03.010 ◽

2015 ◽

Vol 120 ◽

pp. 118-126 ◽

Author(s):

Xiuhui Yang

Keyword(s):

Liquid Crystal ◽

Mach Number ◽

Bounded Domain ◽

Nematic Liquid Crystal ◽

Well Posedness ◽

Low Mach Number ◽

Low Mach Number Limit ◽

Nematic Liquid Crystal Flows ◽

Compressible Nematic Liquid Crystal

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Global well-posedness to the 3D Cauchy problem of compressible non-isothermal nematic liquid crystal flows with vacuum

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2020.103219 ◽

2021 ◽

Vol 58 ◽

pp. 103219

Author(s):

Yang Liu ◽

Xin Zhong

Keyword(s):

Cauchy Problem ◽

Liquid Crystal ◽

Nematic Liquid Crystal ◽

Well Posedness ◽

Nematic Liquid Crystal Flows

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Global Well-Posedness and Temporal Decay Estimates for the 3D Nematic Liquid Crystal Flows

Journal of Mathematical Fluid Mechanics ◽

10.1007/s00021-018-0373-6 ◽

2018 ◽

Vol 20 (4) ◽

pp. 1459-1485 ◽

Author(s):

Qiao Liu

Keyword(s):

Liquid Crystal ◽

Nematic Liquid Crystal ◽

Well Posedness ◽

Decay Estimates ◽

Temporal Decay ◽

Nematic Liquid Crystal Flows

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Well-posedness for 3D nematic liquid crystal flows with damping

Journal of Inequalities and Applications ◽

10.1186/s13660-020-02379-9 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Hui Liu ◽

Chengfeng Sun ◽

Jie Xin

Keyword(s):

Liquid Crystal ◽

Nematic Liquid Crystal ◽

Well Posedness ◽

Nematic Liquid Crystal Flows

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Global well-posedness of non-isothermal inhomogeneous nematic liquid crystal flows

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2020161 ◽

2017 ◽

Vol 22 (11) ◽

pp. 0-0

Author(s):

Dongfen Bian ◽

◽

Yao Xiao ◽

◽

Keyword(s):

Liquid Crystal ◽

Nematic Liquid Crystal ◽

Well Posedness ◽

Nematic Liquid Crystal Flows

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Long-Time Behavior for a Hydrodynamic Model on Nematic Liquid Crystal Flows with Asymptotic Stabilizing Boundary Condition and External Force

SIAM Journal on Mathematical Analysis ◽

10.1137/120866476 ◽

2013 ◽

Vol 45 (3) ◽

pp. 965-1002 ◽

Author(s):

Maurizio Grasselli ◽

Hao Wu

Keyword(s):

Boundary Condition ◽

Liquid Crystal ◽

Nematic Liquid Crystal ◽

External Force ◽

Hydrodynamic Model ◽

Time Behavior ◽

Long Time Behavior ◽

Long Time ◽

Nematic Liquid Crystal Flows

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Global m-Equivariant Solutions of Nematic Liquid Crystal Flows in Dimension Two

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-017-1144-x ◽

2017 ◽

Vol 226 (2) ◽

pp. 767-808 ◽

Author(s):

Yuan Chen ◽

Yong Yu

Keyword(s):

Liquid Crystal ◽

Nematic Liquid Crystal ◽

Nematic Liquid Crystal Flows

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Regularity Criterion for the 3D Nematic Liquid Crystal Flows

ISRN Mathematical Analysis ◽

10.5402/2012/935045 ◽

2012 ◽

Vol 2012 ◽

pp. 1-10 ◽

Author(s):

Jishan Fan ◽

Tohru Ozawa

Keyword(s):

Liquid Crystal ◽

Liquid Crystals ◽

Nematic Liquid Crystal ◽

Regularity Criterion ◽

Hydrodynamic Theory ◽

Nematic Liquid Crystal Flows

We study the hydrodynamic theory of liquid crystals. We prove a logarithmically improved regularity criterion for two simplified Ericksen-Leslie systems.

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