Survey of the Benjamin-Ono Equation with Periodic Boundary Conditions

Explore a comprehensive survey of the Benjamin-Ono equation with periodic boundary conditions in this 1-hour 8-minute seminar presented by Patrick Gérard from Université Paris-Saclay, France. Delve into the dynamics of this nonlinear dispersive wave equation, introduced in 1967 as a model for long internal gravity waves in a two-layer fluid with infinite depth. Learn how the use of a Lax pair provides a complete picture of the equation's behavior, including explicit solution formulas, global well-posedness in sharp regularity, long-time dynamics, and classification of various wave types. Discover insights from joint works with Thomas Kappeler and Petar Topalov, covering topics such as traveling waves, multi-solitons, doubly periodic solutions, and the smoothing effect. Gain valuable knowledge in this online research dissemination event, organized by the Society for Industrial and Applied Mathematics, which aims to recognize achievements in the field and promote the standing of SIMA and APDE.