Orateur
Description
In the first part of this talk, we begin by introducing an explicit solution formula for the Benjamin-Ono (BO) equation obtained by Patrick Gérard. We show how building on this representation yields new tools for understanding the long-time dynamics of BO, both theoretically and numerically.
In the second part, we study the weakly nonlinear evolution of BO starting from a randomized initial data on a large torus. By rescaling and iterating this explicit formula, combined with probabilistic arguments, we obtain insight on the wave-kinetic theory for BO, up to the physically relevant kinetic time scale and across all scaling laws in the kinetic regime. To our knowledge, this provides the first rigorous characterization of wave-kinetic dynamics for a one-dimensional integrable PDE up to these physically relevant timescales.