中科院数学与系统科学研究院
华罗庚数学科学中心
数学研究所
Singularity and Homogenization of PDE 2018
报告人：林芳华 教授 (纽约大学柯朗研究所)
题 目：An Introduction to Elliptic Homogenization
时 间：5月8日 14：30-16：30
5月9日 14：30-16：30
5月11日 14：30-16：30
5月14日 09：30-11：30
5月15日 14：30-16：30
地 点：数学院南楼N202室
摘 要：
I shall started with some examples and problems that concern with partial differential equations in highly oscillating medium. Then we proceed with various classical results of G- and H-convergences, div-curl, oscillating test function and viscosity methods as well as correctors in the periodic case. Applications and further questions will be addressed at end.
报告人：Prof. Changyou Wang (Purdue University)
题 目：On the general theory of blow ups for harmonic maps
时 间：5月14日 09：30-11：30
地 点：数学院南楼N208室
时 间：5月15日 14：30-16：30
地 点：数学院南楼N204室
报告人：刘勇 教授 (华北电力大学)
题 目：Allen-Cahn, Ginzburg-Landau equations and related integrable systems
时 间：5月10日 14：30-16：30
地 点：数学院南楼N208室
摘 要：In this talk, we discuss the construction and analysis of entire solutions of equations including Allen-Cahn, Ginzburg-Landau and several integrable systems, such as Toda, KP-I and elliptic sine-Gordon. We show that these equations have interesting connections.
报告人：徐强 博士(北京大学)
题 目：Convergence rates for elliptic homogenization problems in Lipschitz domain
时 间：5月16日 14：30-16：30
地 点：数学院南楼N202室
摘 要：
In this talk, I plan to study convergence rates in $L^2$ norm for elliptic homogenization problems in Lipschitz domains. It involves some new weighted-type inequalities for the smoothing operator at scale $\varepsilon$, as well as, layer and co-layer type estimates, and the related details will be touched. In order to obtain a sharp result, a duality argument will be imposed. Here we do not require any smoothness assumption on the coefficients, and the main ideas may be extended to other models, such as Stokes systems and parabolic systems, arising in the periodic homogenization theory.
报告人：Prof. Changyou Wang (Purdue University)
题 目：On the general theory of blow ups for harmonic maps
时 间：2018.05.29（星期二），14:30-17:00
地 点：数学院南楼N202室
报告人：Prof. Juncheng Wei (University of British Columbia)
题 目：Gluing methods and finite time blow-ups for harmonic map flows into S2
时 间：2018.06.01（星期五），14:30-16:30
地 点：数学院南楼N202室
摘 要：I will explain the main ideas in the gluing constructions of Type II blow-ups for harmonic map flows into $S^2$: $$ u_t=\Delta u+ |\nabla u|^2 u, u:\Omega \to S^2$$ where $\Omega$ is a smooth two-dimensional domains.
报告人：Prof. Zhongwei Shen (University of Kentucky)
题 目：Regularity Results in Elliptic Homogenization
时 间：2018.05.28（星期一），09:30-11:30
2018.05.30（星期三），14:30-17:00
地 点：数学院南楼N202室
报告人：郑有泉 教授 (天津大学)
题 目：Infinite time blow-up for half-harmonic map flow from into
时 间：2018.05.31（星期四），15:00-16:30
地 点：数学院南楼N208室
报告人： 韦东奕 博士(北京大学)
题 目：Transition threshold for the 3D Couette flow in Sobolev space
时 间：5月31日 14：00-15：00
地 点：数学院南楼N208室
Abstract:In this paper, we study the transition threshold of the 3D Couette flow in Sobolev space at high Reynolds number {Re}. It was proved that if the initial velocity v0 satisfies $\|v_0-(y,0,0)\|_{H^2}\le c_0{Re}^{-1}$, then the solution of the 3D Navier-Stokes equations is global in time and does not transition away from the Couette flow. This result confirms the transition threshold conjecture in physical literatures.
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