Global well-posedness for the dynamical Q-tensor model of liquid crystals

We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is...

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Bibliographic Details
Published inScience China. Mathematics Vol. 58; no. 6; pp. 1349 - 1366
Main Authors Huang, JinRui, Ding, ShiJin
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.06.2015
Subjects
Applications of Mathematics
Computational fluid dynamics
Dynamical systems
Dynamics
Fluid flow
Fluids
Liquid crystals
Mathematical models
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Navier-Stokes方程
向列液晶
张量
模型
流体模拟
解的存在性
连续依赖性
适定性
nematic liquid crystals
global solutions
uniqueness
35R35
35Q30
tensor
76N10
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ISSN1674-7283
1869-1862
DOI10.1007/s11425-015-4990-8

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Summary:We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.
Bibliography:dynamical tensor Stokes parabolic nematic viscosity Navier estimates uniqueness proof
We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.
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ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-015-4990-8