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

报告人：王长友教授(PurdueUniversity)

报告时间：2024年6月18日 上午 9:40-12:00

报告地点：数理楼135

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 with Joshua Kortum, that proves the existence of such a global solution in the axisymmetric setting.

报告人简介：王长友教授是偏微分方程领域的知名专家，国家杰出青年基金（B类）获得者，于1996年在Rice大学获得博士学位，先后在芝加哥大学，肯塔基大学，普渡大学工作。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, ARMA, CMP, Trans. Amer. Math. Soc.等国际高水平期刊发表论文100余篇。