The Cauchy Problem for Dissipative Benjamin-Ono equation in Weighted Sobolev spaces

Abstract

We study the well-posedness in weighted Sobolev spaces, for the initial value problem (IVP) associated with the dissipative Benjamin-Ono (dBO) equation. We establish persistence properties of the solution flow in the weighted Sobolev spaces $\z_{s,r}=H^s(\R)\cap L^2(|x|^{2r}dx)$, $s\ge r>0$. We also prove some unique continuation properties in these spaces. In particular, such results of unique continuation show that our results of well posedness are sharp.

26 pages. In this version we use the Stein-Weiss interpolation theorem with change of measure