时间：2016年6月23日（周四）15：00 - 17:00
地点：数学研究中心学术报告厅
主办：数学与计算机科学学院、福建省分析数学及应用重点实验室、数学研究中心
主讲：美国乔治亚理工学院 林治武教授
专家简介：林治武，男，美国乔治亚理工学院教授、博士生导师，从事非线性分析及其应用领域的研究工作，在非线性波动方程解的稳定性、解的长时间行为方面作出一些列开创性的工作，研究成果发表在《CPAM》、 《CMP》、《ARMA》等学术期刊。
报告摘要：Modulational instability (also called side band instability, Benjamin-Feir instability) is an important instability mechanism in lots of dispersive wave equations, including 2D water waves and many model equations such as KDV, BBM, and Whitham equations. It leads to the breakdown of periodic traveling wave pattern in these modes. In the literature, such instability had been studied a lot from the linearized equation, i.e., the spectra of the linearized operator. With Shasha Liao and Jiayin Jin, we are able to prove nonlinear modulational instability for lots of dispersive models including nonlinear Schrodinger equation, BBM, and KDV type equations (KDV, Benjamin-Ono, Whitham etc). The nonlinear instability is proved for both periodic and localized perturbations. The two main ingredients in the proof are: for the linear step, the semigroup estimates are obtained by using the Hamiltonian structures of the linearized PDEs; for the nonlinear step, the loss of derivative in the nonlinear term is overcome by the construction of higher order approximation solutions or by using a bootstrap argument.