题   目：Global existence and compactness for axisymmetric Ericksen-Leslie system in dimension three

主讲人：王长友 教授

单   位：美国普渡大学

时   间：6月24日16:00

地   点：学院南阶梯教室

摘   要：In this talk, I will discuss the Ericksen-Leslie system, which is the governing equation for the hydrodynamics of nematic liquid crystals, in dimension three. Mathematically, this is a dissipative system strongly coupling between the Navier-Stokes equation for the underlying fluid velocity field and the transported harmonic flow into the unit sphere for the macroscopic orientation field of liquid crystal molecules. Because of the super-critical nonlinearities induced by Ericksen stress tensors, it has been an outstanding open question to establish Leray-Hopf type global solutions for any initial data with finite energy. I will describe a recent work, joint with Joshua Kortum, that proves the existence of such a global solution in the axisymmetric setting.

简   介：王长友，美国Purdue University（普渡大学）数学系终身教授，偏微分方程领域的知名专家，于1996年在Rice大学获得博士学位。研究兴趣包括PDE，几何分析等，主持多项美国自然科学基金，获得荣誉包括：Sloan奖、美国数学会Centennial Fellowship、IMA New Directions奖、Simons Fellowship等。已在CPAM, Arch. Ration. Mech. Anal., Comm. Math. Phys., Trans. Amer. Math. Soc. 等国际高水平期刊发表论文100余篇。