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Pointwise Structures of Some Partial Differential Equations

Speaker

Haitao Wang, Shanghai Jiao Tong University

Time

2017.09.18 14:00-15:00

Venue

601, Pao Yue-Kong Library

Abstract

In this talk, I will review some pointwise results of PDEs that are related to fluid dynamics and kinetic theory. While wellposedness is of the fundamental importance in PDE theory, the pointwise structures of the solution give more quantitative understanding of the underlying physical phenomena. This talk consists of three parts. In the first part, the wave structure of linearzied Landau equation and other generalizations will be presented. The results reveal that the large time behavior is dominated by Naiver-Sotkes type diffusion wave. The regularization effect plays an important role in the estimates. In the second part, we will see how to obtain the pointwise structure for viscous scalar rarefaction wave through Green’s function approach. The result shows the Burgers type waves are universal. Finally, we will discuss the construction of Green’s function for initial-boundary value problem in half space and its applications.

Bio

Haitao Wang, Shanghai Jiao Tong University