报告人：李国鹏（北京理工大学 助理教授）
报告时间：4月22日（周二）16：00-17：00
报告地点：章辉楼442
联系人：王保祥教授
欢迎广大师生参加！
报告摘要：The Intermediate Long Wave equation (ILW) models the internal wave propagation of the interface in a stratified fluid of finite depth, establishing a natural connection between the deep-water regime (the Benjamin-Ono (BO) regime) and the shallow-water regime (the Korteweg-de Vries (KdV) regime). In this talk, I will address convergence issues for ILW from a statistical mechanics viewpoint at different energy levels. By exploiting both the Hamiltonian and completely integrable structure of ILW, BO, and KdV, I will delve into the convergence of Hamiltonian and higher-order conservation laws for ILW, along with their associated measures and dynamics. Two interesting phenomena arise: (i) the modes of convergence of the measures in the deep-water and shallowwater limits differ. (ii) KdV, appearing in the shallow-water limit, possesses half as many conservation laws as ILW and BO, leading to a 2-to-1 collapse phenomenon.
This talk is based on joint works with Tadahiro Oh （Edinburgh）, Andreia Chapouto （Université de Versailles Saint-Quentin)
报告人简介：李国鹏，北京理工大学助理教授。2022年博士毕业于爱丁堡大学。2024年至今在北京理工大学任职。李国鹏教授主要从事于非线性偏微分方程，随机偏微分方程；（确定性和概率性的）非线性色散Hamiltonian偏微分方程的研究。相关论文发表于Nonlinearity，J. Differ. Equations，Math. Res. Lett. , Trans. Lond. Math. Soc.等国际知名杂志。
