中科院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

调和分析和偏微分方程研讨班

报告人：Zexing Li (University of Cambridge)

题  目：On asymptotic stability for self-similar blowup of mass supercritical NLS

时  间：2024.09.02（周一）10：00-11：00

地  点：S803

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.