Weakly Dispersive Internal Waves

by Prof. Miller Peter D. (Department of Mathematics University of Michigan)

Monday 23 Sept 2013, 15:00 → 16:00 Europe/Rome

Aula 6 (Dipartimento di Fisica - Ed. G.Marconi)

Asymptotic models for internal wave motion in 1+1 dimensions include nonlocal linear dispersion terms arising from the elimination of potential flow on one side of the interface via a Dirichlet-Neumann map. Such models include the intermediate long wave equation in the case of finite depth and the Benjamin - Ono (BO) equation in the case of infinite depth (of the lower fluid layer). In some physical situations the dispersive effects are small compared with nonlinear effects that eventually lead to wave breaking, and in this talk, I will describe some of our attempts to study the corresponding problem in the context of the BO equation. In particular, we will present a simple and intuitive weak convergence result (joint work with Z. Xu) that is a consequence of a new analogue of the variational method of Lax and Levermore but that takes as inspiration also the moment expansion method of Wigner in random matrix theory.