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
Published in:Mathematics (Basel) 2021-04, Vol.9 (8), p.912
Main Authors: Li, Sirui, Zhao, Fangxin
Format: Article
Language:English
Subjects:
Crystals
Elastic limit
Elastic properties
Energy
Ericksen–Leslie model
Liquid crystals
Nematic crystals
Phase transitions
Qian–Sheng model
uniaxial limit
Viscosity
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9080912