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

作     者：李进开 辛周平 

作者机构：The Institute of Mathematical SciencesThe Chinese University of Hong KongHong KongChina Department of Computer Science and Applied MathematicsWeizmann Institute of Science Rehovot 76100Israel 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2016年第36卷第4期

页      面：973-1014页

核心收录：

学科分类：07[理学] 070205[理学-凝聚态物理] 08[工学] 080501[工学-材料物理与化学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0703[理学-化学] 0702[理学-物理学] 

基　　金：Hong Kong RGC Earmarked Research Grants 14305315,CUHK4041/11P and CUHK4048/13P The Chinese University of Hong Kong,a Croucher Foundation-CAS Joint Grant,and a NSFC/RGC Joint Research Scheme(N-CUHK443/14) 

主　　题：Global weak solutions non-isothermal nematic liquid crystals 

摘      要：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.