Christophe Charlier: On Boussinesq’s equation for water waves

Abstract:

A century and a half ago, J. Boussinesq derived an equation for the propagation of water waves in a channel. Despite the fundamental importance of this equation for a number of physical phenomena, mathematical results on it remain scarce. One reason for this is that the equation is ill-posed. In this talk, I will discuss a number of new results on the Boussinesq equation, such as existence, uniqueness, blow-up and asymptotic results.

The talk is based on join work with Jonatan Lenells.