Abstract: 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 Andreia Chapouto (Monash University), Ruoyuan Liu (University of Bonn), Tadahiro Oh (University of Edinburgh/BIT).

Bio: Guopeng Li joined the Beijing Institute of Technology (China) as a tenure-track Assistant Professor in October 2024. He completed his PhD at the University of Edinburgh in 2022 and then held a postdoctoral position at the Maxwell Institute for Mathematical Sciences. His research interests lie at the intersection of stochastic analysis, probability, and dispersive partial differential equations.