液晶动力学系统部分正则性和适定性的研究

In this project, we consider part of regularity and well-posedness of the Dynamic Liquid Crystal System. We mainly study how the solution behaves near the singular point , the uniqueness of mild ancient solution in axially symmetric condition and the well-posedness to Q-tensor dynamic system. We mainly use lifting regularity methods, the back uniqueness method to parabolic equations, Liouville Theorem and Fourier analysis methods. It is newly attempt to use the back uniqueness method and Liouville Theorem on Dynamic Liquid Crystal System.

本项目考虑液晶动力学系统的部分正则性与适定性，主要研究Erickson-Lieslie动力学系统的奇性增长，轴对称情形弱解的唯一性和Ｑ-张量动力学系统的适定性。所用的方法有正则提升法，抛物型方程解的后向唯一性证明方法，Liouville定理和常规的傅里叶分析方法。其中对液晶方程应用抛物型方程解的后向唯一性证明方法和Liouville定理是新的尝试.