Thursday, 15 October 2026, 4-5pm Location: Medical Sciences and Anatomy, Anatomy G29 J Z Young LT

• Speaker: Patrick Gérard (Université Paris Saclay)
  
  Title: The Benjamin-Ono equation on the line as an integrable system.
  
  Abstract:
The description of evolution phenomena occupies an important place in Mathematical Physics. Beyond the existence and the uniqueness for the initial value problem, an important issue is the classification of long-time behaviours, which is difficult because it requires a precise access to solutions. There is however a class of evolutions for which this access is made possible through the so-called integrable structure of the equation. In this talk, I will survey this notion of integrability by discussing a model from fluid dynamics which recently received a considerable attention : the Benjamin-Ono equation on the real line. In particular, I will try to explain how a new representation formula allows to describe the long-time behaviour of solutions for a broad class of initial data.

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