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。