主讲人简介：上海交通大学讲席教授、国家特聘专家，国务院学位委员会第八届学科评议组成员、美国数学会会士、DCDS等杂志编委。在流体力学、几何分析、局部和非局部偏微分方程组等方面开展研究。与合作者研究了三维N-S方程大初值问题的全局稳定性；对Benjamin-Feir非稳定性进行了稳定化；得到一类重要的曲率方程解的对称性及分类；解决了球对称函数的Nirenberg 问题；得到了变号曲率方程解的先验估计；发展了积分形式的移动平面法；证明了一系列极大值原理；成果发表于Ann. of Math、Invent. Math、CPAM、PNAS等重要学术杂志。共发表SCI论文80余篇，SCI引用4000多次。

内容摘要：Here, we focus on maximum principles, Liouville type theorems, classi cation of solutions and give a brief introduction of some problems and results on qualitative study of some nonlinear elliptic type PDEs.

We start with some recent work on the incompressible Navier- Stokes and Euler equations and give a short introduction of some re- lated methods, and some results with applications. Then, we focus on the Hardy-Littlewood-Sobolev system and curvatures related geomet- ric equations as examples to illustrate the ideas, methods and possible applications.

主持人：秦玉明

撰写：李学元