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——澳门沙金在线平台建校70周年系列学术活动

报告题目: Deep-water and shallow-water limits of statistical equilibria for the intermediate long wave equation

报告人: 李国鸟 博士（爱丁堡大学）

Abstract

The intermediate long wave equation (ILW) models the internal wave propagation of the interface in a stratified fluid of finite depth, providing a natural connection between the deep-water regime (= the Benjamin-Ono (BO) regime) and the shallow-water regime (= the KdV regime). In this talk, I will discuss convergence problems for ILW from a statistical viewpoint, at different energy levels.

By exploiting both Hamiltonian and completely integrable structure of ILW (and also of BO and KdV), I will discuss convergence of Hamiltonian/higher order conservation laws for ILW, their associated measures and their associated dynamics. In particular, our results give two interesting phenomenons: (i) modes of convergence of the measures in the deep water and shallow-water limits are different. (ii) KdV, appearing in the shallow-water limit, possesses half as many conservation laws as ILW and BO and thus there is an 2-to-1 collapse of ILW conservation laws to those of KdV.

This talk is based on joint works with Tadahiro Oh, Andreia Chapouto (both Edinburgh) and Guangqu Zheng (Liverpool).

报告时间：2023年10月19日（周四）16：00-17：00

报告地点：教二楼913

联系人：高传伟