报告题目：Global existence and compactness for axisymmetric Ericksen-Leslie system in dimension three

报 告 人：王长友教授（普渡大学）

报告时间：2024年6月19日  16:00

报告地点：格物楼数学研究中心528

报告摘要：

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 withJoshua Kortum, that proves the existenceof such a global solution in the axisymmetric setting.

报告人简介：

王长友，美国Purdue University（普渡大学）数学系终身教授，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：S1oan奖、美国数学会Centennia1 Fe1lowship、IMA New Directions奖、Simons Fellowship等。在CPAM, Arch. Ration. Mech. Ana1., Comm. Math. Phys.，Trans. Amer. Math. Soc.等国际高水平期刊发表论文100余篇。