【学术报告】2017年6月12日下午金嘉寅博士来我院举办学术讲座

2017-06-12 15:14:48    浏览次数:0

报告人:金嘉寅(Georgia Institute of Technology)
报告题目:Nonlinear modulational instability of periodic traveling waves for several dispersive PDEs.
报告摘要:We prove nonlinear modulational instability for both periodic and localizedperturbations of periodic traveling waves for several dispersive PDEs,including the KDV type equations (e.g. the Whitham equation, the generalizedKDV equation, the Benjamin-Ono equation), the nonlinear Schr\"{o}dingerequation and the BBM equation. First, the semigroup estimates required for thenonlinear proof are obtained by using the Hamiltonian structures of thelinearized PDEs; Second, for KDV type equations the loss of derivative in thenonlinear term is overcome in two complementary cases: (1) for smoothnonlinear terms and general dispersive operators, we construct higher orderapproximation solutions and then use energy type estimates; (2) for nonlinearterms of low regularity, with some additional assumption on the dispersiveoperator, we use a bootstrap argument to overcome the loss of derivative.This is a joint work with Shasha Liao and Zhiwu Lin.2. Classifications of local dynamics near solitary waves for several Hamiltonian PDEs I &IIIn this series of talks, we classify the dynamics near solitary waves for Hamiltonian PDEs, including the Gross-Pitaevskii equation and the supercritical gKDV equations, by constructing  local invariant manifolds for the solitary waves. There are two main difficulties: (1) How to decompose the energy space along the orbits of solitary waves smoothly ; (2) The nonlinearity does not map energy space to energy space and we need to derive suitable space-time estimates. This is joint work with Zhiwu Lin and Chongchun Zeng.
报告时间:2017年6月12日(星期一)下午16:00-17:00
报告地点:科技楼南楼702学术报告厅