Simplified The Lcd Equations Global Existence Of Weak Solutions To Prove

The continuum theory of liquid crystals due to Ericksen and Leslie was developed during the period of 1958 through 1968.Since then there has been a remarkable increase in liquid crystal research in both theoretical and experimental aspects.The Ericksen-Leslie theory has successfully predicted several effects and analyzed many others rather well.Most analytical work,however,has been carried out under rather special assumptions concerning either the type of flow or the form of the solutions.Such methods,though valuable,are inadequate for investigating many fundamental questions.We study a simplified system which retains most of the interesting mathematical properties of the equations for the flow of Nematic Liquid Crystals.This is a coupled nonparabolic dissipative dynamic system.We derive the basic energy laws which enable us to prove the global existence of the weak solutions.We also discuss some blowup behavior of smooth solutions.This paper is organized in the following way:In chapter 1,the history and the latest developments are introduced,as well as the basic energy law of the system.In chapter 2,we use the fixed point method to gain a sequence of approximated solutions.In chapter 3,by passing the approximated solutions to the limit,we give the proof of the existence of global weak solutions.In chapter 4,we give a brief proof of blowup behavior of smooth solutions to equations for Nematic Liquid Crystal.