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

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

2010-04-30

arxiv.org/abs/1004.5592v2

Mathematics

Analysis of PDEs

21 pages

Scientific paper

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 $Z_{s,r}=H^s(\R)\cap L^2(|x|^{2r}dx)$, $s\in\R, \,s\geq 1$ and $s\geq r$. 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.

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