Singularity and Homogenization of PDE 2018

目：An Introduction to Elliptic Homogenization

间：58 1430-1630

59 1430-1630

511 1430-1630

5月14日 09：30-11：30

5月15日 14：30-16：30

点：数学院南楼N202

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.

目：On the general theory of blow ups for harmonic maps

间：5月14日 09：30-11：30

点：数学院南楼N208

间：5月15日 14：30-16：30

点：数学院南楼N204室

目：Allen-Cahn, Ginzburg-Landau equations and related integrable systems

间：5月10日 14：30-16：30

点：数学院南楼N208

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.

目：Convergence rates for elliptic homogenization problems in Lipschitz domain

间：516 1430-1630

点：数学院南楼N202

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.

2018.05.30（星期三），14:30-17:00

目：Transition threshold for the 3D Couette flow in Sobolev space

间：531 1400-1500

点：数学院南楼N208

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.