Andreia Chapouto (Versailles)

Deep- and shallow-water limits of statistical equilibria for the intermediate long wave equation.

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 BO regime) and the shallow-water regime (= the KdV regime). Exploiting the complete integrability of ILW, I will discuss the statistical convergence of ILW to both BO and KdV, namely the convergence of the higher order conservation laws for ILW and their associated invariant measures. In particular, as KdV possesses only half as many conservation laws as ILW and BO, we observe a novel 2-to-1 collapse of ILW conservation laws to those of KdV, which yields alternative modes of convergence for the associated measures in the shallow-water regime.

This talk is based on joint work with Guopeng Li and Tadahiro Oh.