Energy transfer and Generalized Fermi's Golden Rule in Hamiltonian nonlinear Klein-Gordon equations

报告人：雷震 (复旦大学)

时  间： 2023年3月1日  下午 4：30- 5：30

地  点： 数学楼2-3会议室

Abstract: More than 20 years ago, Soffer-Weinstein considered a class of nonlinear Klein-Gordon equations with nice potentials. For the first time they proved that spatially localized and time-periodic solutions of the linear problem are destroyed by generic nonlinear Hamiltonian perturbations via slow radiation of energy to infinity, via energy transfer from the discrete to continuum modes, under the condition that the discrete modes are close to the continuous spectral modes. Since then, a long-standing open question is to study the the corresponding problem with small eigenvalues, which was in also raised in the paper of Soffer-Weinstein 1999. In this talk, we will report our recent result on this problem which settles the above open question. This is a joint work with my students Jie Liu and Zhaojie Yang.

报告人简介： 雷震， 复旦大学数学科学学院副院长，国家杰出青年科学基金获得者、国家级人才计划入选者。长期在流体力学领域从事前沿基础理论研究，提出了“强零条件”的概念，发现了不可压流体的非线性内蕴结构并独自建立了不可压弹性与粘弹方程组解的整体稳定性理论，在不可压 NS方程组等领域有杰出贡献,获得了菲尔茨奖得主Bourgain、陶哲轩、阿贝尔奖及沃尔夫奖得主Sinai等国际数学大家的高度评价。2020年获国家自然科学奖二等奖(排名第1)，2022年荣获第四届“科学探索奖”。