The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals

The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals

In this article, we consider the Qian–Sheng model in the Landau–de Gennes framework describing nematic liquid crystal flows when the inertial effect is neglected. By taking the limit of elastic constant to zero (also called the uniaxial limit) and utilizing the so-called Hilbert expansion method, we...

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Bibliographic Details
Main Authors: Sirui Li, Fangxin Zhao
Format: Article
Language:English
Published: MDPI AG 2021-04-01
Series:Mathematics
Subjects:
liquid crystals
Qian–Sheng model
Ericksen–Leslie model
uniaxial limit
Online Access:https://www.mdpi.com/2227-7390/9/8/912
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spelling doaj-77660533a7cb47c9b75beb4e460cce542021-04-20T23:03:24ZengMDPI AGMathematics2227-73902021-04-01991291210.3390/math9080912The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid CrystalsSirui Li0Fangxin Zhao1School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, ChinaSchool of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaIn this article, we consider the Qian–Sheng model in the Landau–de Gennes framework describing nematic liquid crystal flows when the inertial effect is neglected. By taking the limit of elastic constant to zero (also called the uniaxial limit) and utilizing the so-called Hilbert expansion method, we provide a rigorous derivation from the non-inertial Qian–Sheng model to the Ericksen–Leslie model.https://www.mdpi.com/2227-7390/9/8/912liquid crystalsQian–Sheng modelEricksen–Leslie modeluniaxial limit
collection DOAJ
language English
format Article
sources DOAJ
author Sirui Li
Fangxin Zhao
spellingShingle Sirui Li
Fangxin Zhao
The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals
Mathematics
liquid crystals
Qian–Sheng model
Ericksen–Leslie model
uniaxial limit
author_facet Sirui Li
Fangxin Zhao
author_sort Sirui Li
title The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals
title_short The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals
title_full The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals
title_fullStr The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals
title_full_unstemmed The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals
title_sort uniaxial limit of the non-inertial qian–sheng model for liquid crystals
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-04-01
description In this article, we consider the Qian–Sheng model in the Landau–de Gennes framework describing nematic liquid crystal flows when the inertial effect is neglected. By taking the limit of elastic constant to zero (also called the uniaxial limit) and utilizing the so-called Hilbert expansion method, we provide a rigorous derivation from the non-inertial Qian–Sheng model to the Ericksen–Leslie model.
topic liquid crystals
Qian–Sheng model
Ericksen–Leslie model
uniaxial limit
url https://www.mdpi.com/2227-7390/9/8/912
work_keys_str_mv AT siruili theuniaxiallimitofthenoninertialqianshengmodelforliquidcrystals
AT fangxinzhao theuniaxiallimitofthenoninertialqianshengmodelforliquidcrystals
AT siruili uniaxiallimitofthenoninertialqianshengmodelforliquidcrystals
AT fangxinzhao uniaxiallimitofthenoninertialqianshengmodelforliquidcrystals
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