中文摘要：

对于上世纪80年代中期以来液晶模型的数学理论方面的研究进行了综述．首先论述了静态模型的研究进展，其中包括经典的Oseen-Frank理论、Ericksen理论以及最近成为研究热点的Q—tensor理论，重点介绍其中的变分问题极小元的存在性和奇性分析以及从向列相到近晶相的相变理论．随后介绍了近年来对于液晶的发展理论即Erickson-Leslie理论的研究，包括不可压缩模型的解的存在性和部分正则性、可压缩模型的适定性理论．同时对液晶模型今后可能的研究课题进行了探讨和展望．

英文摘要：

This is a survey on the mathematical studies of liquid crystals since the middle of 1980＇s. First of all, the development of the mathematical researches on the static models is introduced. And the singularity theory of the solutions to the static variational problem is discussed. Then it is concerned with the phase transition from nematic phase to smectic phase. Subsequently, the dynamical models, Ericksen-Leslie models are discussed. The development on the researches of well-posedness for the incompressible and compressible Ericksen-Leslie models is given. Some unsolved problems are also stated.