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A review of Soffer-Weinstein's proof of instability in Hamiltonian, resonant nonlinear wave equations

组织者

拉尔斯•安德森 , 皮特·布鲁 , Siyuan Ma , 于品

演讲者

张笑然

时间

2024年11月06日 10:00 至 12:00

地点

Tsinghua-Jingzhai-105

线上

Zoom 518 868 7656 (BIMSA)

摘要

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.