Por Andreia Chapouto (University of Edinburgh).

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 two famous water-wave equations: the Benjamin-Ono equation (= the deep-water regime) and the Korteweg-de Vries equation (= the shallow-water regime). I will discuss how to exploit the completely integrable nature of the equation to establish the statistical convergence of ILW to both BO and KdV, namely, the convergence of the higher order conservation laws for ILW and of their associated invariant measures. Here, we observe a stark contrast between the two regimes, with distinct modes of convergence as well as a novel 2-to-1 collapse of the invariant ILW dynamics to the corresponding invariant KdV dynamics.

Transmissão via Zoom (pw: lisbonwade).

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.