Sharp well-posedness results of the Benjamin-Ono equation in Hs(T,R) and qualitative properties of its solutions
Speaker:
Thomas Kappeler, Universität Zurich
Date and Time:
Tuesday, October 6, 2020 - 10:00am to 10:45am
Location:
Online
Abstract:
In this talk I will discuss well-posedness results of the Benjamin-Ono (BO) equation on the torus in the Sobolev
spaces Hs for s>−1/2 with s=−1/2 being the critical Sobolev exponant. The result is sharp
in the sense that the BO solution map does not extend continuously to Hs for s≤−1/2.
Our method of proof can also be used to analyze regularity properties of the solution map and to show
that the constructed solutions are almost periodic in time and that their orbits are relatively compact.
This is joint work with Patrick G\'erard and Peter Topalov. T.K. partially supported by the Swiss National Science
Foundation (project number 200020-165537). P.T. partially supported by the Simons Foundation (award number 526907).
