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On the scaling limit of Onsager's molecular model for liquid crystals
作者:    时间:2018-11-29 浏览次数:

  

报告人:刘豫宁

工作单位:上海纽约大学

报告时间: 12月1日15:00

报告地点:数学与统计学院一楼报告厅

报告摘要:

We study the small Deborah number limit of the Doi-Onsager equation for the dynamics of nematic liquid crystals. This is a Smoluchowski-type equation that characterizes the evolution of a number density function, depending upon both particle position and its orientation vector, which lies on the unit sphere. We prove that, in the low temperature regime, when the Deborah number tends to zero, the family of solutions with rough initial data near local equilibria will converge to a local equilibrium distribution prescribed by a weak solution of the harmonic map heat flow into the sphere. This flow is a special case of the gradient flow to the Oseen-Frank energy functional for nematic liquid crystals and the existence of its global weak solution was first obtained by Y.M Chen, using Ginzburg-Landau approximation. Our result can be considered as a kinetic proof of this classical result. The key ingredient is to show the strong compactness of the family of number density functions and the proof relies on the strong compactness of the corresponding second moment (or the Q-tensor), a spectral decomposition of the linearized operator near the limit local equilibrium distribution, as well as the energy dissipation estimate. This is a joint work with Wei Wang in Zhejiang university.

报告人简介:

刘豫宁,博士,现任上海纽约大学数学助理教授。分别于2006年,2008年在武汉大学学士和硕士学位,2011年在法国南希第一大学获得博士学位。2012-2014年在德国雷根斯堡大学做博士后。2014年起任上海纽约大学数学助理教授。其研究领域为偏微分方程及其在流体力学中的应用。其代表作发表于Archive for Rational Mechanics and Analysis,journal of functional analysis等期刊。