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Waves, gravitation and geometry
A review of Soffer-Weinstein's proof of instability in Hamiltonian, resonant nonlinear wave equations
A review of Soffer-Weinstein's proof of instability in Hamiltonian, resonant nonlinear wave equations
Organizers
Lars Andersson
, Pieter Blue
, Siyuan Ma
, Pin Yu
Speaker
Time
Wednesday, November 6, 2024 10:00 AM - 12:00 PM
Venue
Tsinghua-Jingzhai-105
Online
Zoom 518 868 7656
(BIMSA)
Abstract
We will give a review of Soffer, Weinstein's work[Invent. math. 1999]. They consider a class of nonlinear Klein-Gordon equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. They showed that, for generic nonlinear Hamiltonian perturbations, all small amplitude solutions decay to zero as time tends to infinity at an anomalously slow rate. In particular, spatially localized and time-periodic solutions of the linear problem are destroyed by generic nonlinear Hamiltonian perturbations via slow radiation of energy to infinity.