双曲液晶模型动力学方程的分析问题

本项目致力于双曲型液晶模型动力学方程的分析问题，将着重研究如下问题：一、双曲液晶Ericksen-Leslie方程组光滑解的整体时间适定性；二、双曲液晶Ericksen-Leslie方程组弱解的整体时间存在性；三、从双曲到抛物液晶Ericksen-Leslie方程组的零惯性极限问题；四、可压缩液晶Ericksen-Leslie方程组的相应问题.

This program investigates the analytic problems of the dynamic equations of hyperbolic liquid crystal models. It will focus on the following problems: 1. Global in time well-posedness of the hyperbolic Ericksen-Leslie equations in the context of classical solutions; 2. Global in time well-posedness of the hyperbolic Ericksen-Leslie equations in the context of weak solutions; 3. The zero inertial limit from hyperbolic to parabolic Ericksen-Leslie equations; 4. The corresponding problems in the compressible Ericksen-Leslie equations.