On asymptotic stability for self-similar blowup of mass supercritical NLS
数学专题报告
报告题目(Title)：On asymptotic stability for self-similar blowup of mass supercritical NLS
报告人(Speaker)：Dr. Zexing Li (University of Cambridge)
地点(Place)：北京师范大学后主楼1223
时间(Time)：15：00-16：00, August 27(周二)，2024
邀请人(Inviter)：徐桂香
报告摘要
For slightly mass supercritical semilinear Schrodinger equations, self-similar blowup has been proven to exist and generate stable blowup dynamics, but a detailed asymptotic structure was missing. We will discuss two results leading to the asymptotic stability. Firstly we prove a finite codimensional version by introducing Strichartz estimate for the linearized matrix operator; and secondly, in a forthcoming work, we count all the unstable directions of the matrix operator and then prove the asymptotic stability without losing codimensions. New techniques are introduced to determine the spectrum for such non-self-adjoint and non-relatively-bounded perturbed operator in high dimensions, which might be useful in other context as well.
主讲人简介
Zexing Li is a PhD student in University of Cambridge supervised by Prof. Pierre Raphaël. He is interested in singularity formation and long time dynamics for nonlinear dispersive or dissipative models.
