关于举行陈泓旭博士学术报告的通知

报告主题: Asymptotic behavior and regularity theory of the boundary value problem to the Boltzmann equation

报 告 人: 陈泓旭（香港中文大学）

报告时间：2025年 12月29日（星期一）下午3:30-4:30

报告地点：37号楼3A02

邀 请 人: 杨东成 副教授

欢迎广大师生前往！

                                                                数学学院

2025年12月28日

报告摘要：

In this talk, I will discuss the boundary value problem of the Boltzmann equation. Generally, the kinetic equation exhibits singularities near the boundary.

In the first part of my talk, I will tackle the singularity issue by introducing a kinetic weight and establishing some weighted regularity. In the second part, I will focus on the asymptotic behavior in the infinite layer domain $R^2\times (-1,1)$. Due to the singularities near the boundary, the high-order energy method is not applicable. We propose a spectral method through Fourier transform in the horizontal direction. Our result demonstrate that the solution to the 2D heat equation with a specific diffusion coefficient can be an asymptotic profile of the corresponding 3D Boltzmann solution with a remainder decaying much faster.

报告人介绍：

陈泓旭，香港中文大学数学学院博士后。2022年毕业于威斯康星大学麦迪逊分校。主要从事偏微分方程的研究工作，研究方向是动理学方程和流体力学方程。部分成果发表在Arch. Ration. Mech. Anal., Math. Ann., SIAM J. Math. Anal. 等国际数学期刊。