Mathematical Analysis for the Models of Liquid Crystals

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.