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20201120 杜亨荣 Weak compactness of nematic liquid crystal flows in 2D

发布时间:2020-11-17 10:59    浏览次数:    来源:

【线上学术报告】
报告时间:北京时间11月20日(星期五)上午9:00-10:00
腾讯会议 ID:954 368 397
Title: Weak compactness of nematic liquid crystal flows in 2D
Abstract: In this talk, I will discuss the weak compactness property of solutions to the Ericksen--Leslie system modeling the hydrodynamics of nematic liquid crystals in 2D. The system can be viewed as a coupling between the Navier--Stokes equations for velocity fields and the heat flows of harmonic maps for director fields via a highly nonlinear quadratic term called the Ericksen stress tensor. We show that a kind of "concentration cancellation" occurs in weak solution sequences to the Ericksen--Leslie system and its Ginzburg--Landau type approximation. Roughly speaking, it says that the Ericksen stress terms are insensible to concentrations of director energy so that we can pass the weak limit despite the appearance of singularities. The proof is based on the $L^p$-estimate of the Hopf differential and the Pohozaev type argument. This is a joint work with Tao Huang(Wayne State) and Changyou Wang(Purdue).

报告人简介:杜亨荣,硕士毕业于北京师范大学,师从李杰权教授,现在是普渡大学在读PhD,师从王长友教授,博士阶段的主要研究方向是变分法、几何测度论和偏微分方程,特别是流体动力系统和几何流方面的方程。杜亨荣在读博士期间已写出7篇在相关方向很有意义的论文,其中已经有论文发表在ARMA等著名期刊上。

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