学术报告(Jin Woo Jang 10.12)

Vanishing angular singularity limit to the hard-sphere Boltzmann equation

发布人:杨晓静 发布日期:2023-09-14
主题
Vanishing angular singularity limit to the hard-sphere Boltzmann equation
活动时间
-
活动地址
腾讯会议: 438-226-283
主讲人
Jin Woo Jang 教授 浦项科技大学
主持人
周玉龙

In this talk we study Boltzmann's collision kernel for inverse power law interactions $U_s(r)=1/r^{s-1}$ for $s>2$ in dimension $d=3$. We prove the limit of the noncutoff kernel to the hard-sphere kernel and give precise asymptotic formulas of the singular layer near $\theta\simeq 0$ in the limit $s\to \infty$. Consequently, we show that solutions to the homogeneous Boltzmann equation converge to the respective solutions weakly in $L^1$ globally in time as $s\to \infty$.