# Classical and Quantum Integrability

Sep 2 – 6, 2019
Institut de Mathématiques de Bourgogne
Europe/Paris timezone

## On Birkhoff coordinates of the Benjamin-Ono equation on the torus and applications to solutions with negative Sobolev regularity. Part 2

Sep 2, 2019, 11:00 AM
45m
Amphi Niepce

### Speaker

Thomas Kappeler (University of Zurich)

### Description

In this talk I report on joint work with Patrick Gérard and Peter Topalov concerning properties of the flow map of the Benjamin-Ono equation on the torus. The main result says that the flow map, introduced in our previous work on the space $L^2_{r,0}$ of real valued, $2\pi-$periodic $L^2-$functions with mean $0$,
can be extended to the Sobolev spaces $H^{-s}_{r,0}$ for $0 < s < 1/2$. The key ingredient is a corresponding extension of the Birkhoff coordinates to these Sobolev spaces.

### Primary author

Thomas Kappeler (University of Zurich)

### Presentation materials

There are no materials yet.