Classical and Quantum Integrability

2-6 September 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

2 Sep 2019, 11:00
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)

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