Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions
数学专题报告
报告题目(Title)：Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions
报告人(Speaker)：Tao Zhou (National University of Singapore)
地点(Place)：后主楼1124
时间(Time)：2025年2月28日周五，15:00-16:00
邀请人(Inviter)：徐桂香
报告摘要
In three dimensions, the parabolic-elliptic Keller-Segel system exhibits a rich variety of singularity formations. Notably, it admits an explicit self-similar blow-up solution whose radial stability, conjectured more than two decades ago in [Brenner-Constantin-Kadanoff-Schenkel-Venkataramani, 1999], was recently confirmed by [Glogić-Schörkhuber, 2024]. This paper aims to extend the radial stability to the nonradial setting, building on the finite-codimensional stability analysis in our previous work [Li-Zhou, 2024]. The main input is the mode stability of the linearized operator, whose nonlocal nature presents challenges for the spectral analysis. Besides a quantitative perturbative analysis for the high spherical classes, we adapted in the first spherical class the wave operator method of [Li-Wei-Zhang, 2020] for the fluid stability to localize the operator and remove the known unstable mode simultaneously. Our method provides localization beyond the partial mass variable and is independent of the explicit formula of the profile, so it potentially sheds light on other linear nonlocal problems. This talk is based on the joint work with Zexing Li.
主讲人简介
周涛，新加坡国立大学博士，导师姚珧教授，研究方向集中在来自于生物数学和流体力学中的偏微分方程。
