Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium

Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium

Abstract We consider the inertial Qian–Sheng’s Q-tensor dynamical model for the nematic liquid crystal flow, which can be viewed as a system coupling the hyperbolic-type equations for the Q-tensor parameter with the incompressible Navier–Stokes equations for the fluid velocity. We prove the existenc...

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Main Authors: Xiaoyuan Wang, Sirui Li, Tingting Wang
Format: Article
Language:English
Published: SpringerOpen 2021-02-01
Series:Boundary Value Problems
Subjects:
Liquid crystals
Qian–Sheng’s inertial system
Q-tensor
Local strong solutions
Online Access:https://doi.org/10.1186/s13661-021-01498-6
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spelling doaj-837164f7d0584b66a5f5a2e9e43474852021-02-23T10:37:02ZengSpringerOpenBoundary Value Problems1687-27702021-02-012021111510.1186/s13661-021-01498-6Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibriumXiaoyuan Wang0Sirui Li1Tingting Wang2School of Mathematics and Statistics, Guizhou UniversitySchool of Mathematics and Statistics, Guizhou UniversitySchool of Mathematics and Statistics, Guizhou UniversityAbstract We consider the inertial Qian–Sheng’s Q-tensor dynamical model for the nematic liquid crystal flow, which can be viewed as a system coupling the hyperbolic-type equations for the Q-tensor parameter with the incompressible Navier–Stokes equations for the fluid velocity. We prove the existence and uniqueness of local in time strong solutions to the system with the initial data near uniaxial equilibrium. The proof is mainly based on the classical Friedrich method to construct approximate solutions and the closed energy estimate.https://doi.org/10.1186/s13661-021-01498-6Liquid crystalsQian–Sheng’s inertial systemQ-tensorLocal strong solutions
collection DOAJ
language English
format Article
sources DOAJ
author Xiaoyuan Wang
Sirui Li
Tingting Wang
spellingShingle Xiaoyuan Wang
Sirui Li
Tingting Wang
Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium
Boundary Value Problems
Liquid crystals
Qian–Sheng’s inertial system
Q-tensor
Local strong solutions
author_facet Xiaoyuan Wang
Sirui Li
Tingting Wang
author_sort Xiaoyuan Wang
title Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium
title_short Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium
title_full Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium
title_fullStr Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium
title_full_unstemmed Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium
title_sort local well-posedness of the inertial qian–sheng’s q-tensor dynamical model near uniaxial equilibrium
publisher SpringerOpen
series Boundary Value Problems
issn 1687-2770
publishDate 2021-02-01
description Abstract We consider the inertial Qian–Sheng’s Q-tensor dynamical model for the nematic liquid crystal flow, which can be viewed as a system coupling the hyperbolic-type equations for the Q-tensor parameter with the incompressible Navier–Stokes equations for the fluid velocity. We prove the existence and uniqueness of local in time strong solutions to the system with the initial data near uniaxial equilibrium. The proof is mainly based on the classical Friedrich method to construct approximate solutions and the closed energy estimate.
topic Liquid crystals
Qian–Sheng’s inertial system
Q-tensor
Local strong solutions
url https://doi.org/10.1186/s13661-021-01498-6
work_keys_str_mv AT xiaoyuanwang localwellposednessoftheinertialqianshengsqtensordynamicalmodelnearuniaxialequilibrium
AT siruili localwellposednessoftheinertialqianshengsqtensordynamicalmodelnearuniaxialequilibrium
AT tingtingwang localwellposednessoftheinertialqianshengsqtensordynamicalmodelnearuniaxialequilibrium
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