GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS IN 2D

In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the es...

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Bibliographic Details
Published inActa mathematica scientia Vol. 36; no. 4; pp. 973 - 1014
Main Author 李进开 辛周平
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2016
The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Hong Kong, China
Department of Computer Science and Applied Mathematics, Weizmann Institute of Science Rehovot 76100, Israel%The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Hong Kong, China
Subjects
35D30
76A15
Approximation
Derivatives
Global weak solutions
Inequalities
Landau
Liquid crystals
Mathematical analysis
Nematic crystals
nematic liquid crystals
non-isothermal
Two dimensional
二维
二阶导数
向列相液晶
弱解
整体存在性
近似系统
非等温
35D30
nematic liquid crystals
Global weak solutions
non-isothermal
76A15
Online AccessGet full text
ISSN0252-9602
1572-9087
DOI10.1016/S0252-9602(16)30054-6

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Summary:In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many ＂singular＂ times, at which the energy concentration occurs and the director field losses its second order derivatives.
Bibliography:Global weak solutions; non-isothermal; nematic liquid crystals
In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many ＂singular＂ times, at which the energy concentration occurs and the director field losses its second order derivatives.
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ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(16)30054-6