The IVP for the Benjamin-Ono equation in weighted Sobolev spaces

Abstract

We study the initial value problem associated to the Benjamin-Ono equation. The aim is to establish persistence properties of the solution flow in the weighted Sobolev spaces $Z_{s,r}=H^s(\mathbb{R})\cap L^2(|x{|}^{2r}dx)$, $s\in \mathbb{R},s\ge 1$ and $s\ge r$. We also prove some unique continuation properties of the solution flow in these spaces. In particular, these continuation principles demostrate that our persistence properties are sharp.

21 pages