勷勤数学•专家报告

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

报  告  人：王长友   教授  (邀请人：丁时进 )

                                     Purdue University

时      间：6月12日  15：30-16：30

地     点：数科院西楼111报告厅

报告人简介:

       王长友，美国Purdue University（普渡大学）数学终身教授，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。

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.

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