Research-Zero-dispersion limit for the Benjamin-Ono equation on the torus

Research

PDE Seminar

Zero-dispersion limit for the Benjamin-Ono equation on the torus

Speaker: Louise Gassot（Université de Rennes）
Time: Sep 20, 2023, 16:00-17:00
Location: Zoom：918 0193 7273 ，Password:150170

Abstract

We discuss the zero-dispersion limit for the Benjamin-Onoequation on the torus given a bell-shaped initial data. We provethat the solutions admit a weak limit as the dispersion parametertends to zero which is explicit and constructed from the Burgersequation. The approach relies on the complete integrability forthe Benjamin-Ono equation from Gerard, Kappeler and Topalovand also on the spectral study of the Lax operator associated tothe initial data in the zero-dispersion limit.