Static and Dynamic Theories of Liquid Crystals

Abstract

The study of liquid crystals gives rise to many fascinating but difficult mathematical problems. The purpose of this paper is to briefly summarize some recent advances, as well as to describe the present state of art of the theory of liquid crystals. For the static theory, we emphasis on the theory of defects and the theory of Smectic A materials. We will also study the Ericksen-Leslie theory for the liquid crystal flow. The well-posedness as well as the motion of the defects will be discussed.