Integrability of the Benjamin--Ono equation and applications

Abstract: I will review recent results about the dynamics of the Benjamin--Ono equation on the torus : sharp wellposedness in the Sobolev spaces, almost periodicity of solutions, stability of traveling waves, existence of singular time periodic solutions. All these results are obtained as consequences of the construction of a nonlinear Fourier transformation which is inherited from the Lax pair structure of the equation. I will sketch the construction of this transformation and discuss work in progress about it.

This talk is based on a series of joint works with Thomas Kappeler (Zuerich) and Peter Topalov (Boston).

analysis of PDEs

Audience: researchers in the topic

PDE seminar via Zoom