本项目研究材料科学中涌现出的非线性偏微分方程相关问题，主要研究动力学液晶模型中的正则性关联问题。正则性问题对于弱解与强解的研究、以及解的唯一性等都有重要影响。针对动力学液晶方程组，本项目拟考察（1）解的部分正则性方面，特别是指关于空间变量的正则性，探讨局部正则性的判别条件；（2）解的演化行为，譬如考察解的渐近紧性、整体吸引子、以及解的衰减估计等；（3）正则性准则方面，考察解破裂时刻的奇异类型等。

We are concerned with problems related to the regularity of solutions in partial differential equations, especially the hydrodynamical liquid crystal equations deduced from the material science. Regularity problems are important in the study of weak and strong solutions, and also uniqueness of solutions. For the hydrodynamical liquid crystal equations, we shall study (1) partial regularity problem, which means regularity with respect to the spatial variable: suitable conditions which would result in local regularity; (2) asymptotic behavior problem: such as asymptotic compactness, global attractors, and decay estimate; (3) regularity criteria problem, such as the singularity type at the blow up time, etc.