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Journal of Dynamics and Differential Equations

, Volume 25, Issue 4, pp 907–923 | Cite as

On Decay Properties of Solutions to the IVP for the Benjamin–Ono Equation

  • Cynthia Flores
Article

Abstract

In this work we investigate unique continuation properties of solutions to the initial value problem associated to the Benjamin–Ono equation in weighted Sobolev spaces \(Z_{s,r}=H^s(\mathbb R )\cap L^2(|x|^{2r}dx)\) for \(s\in \mathbb R \), and \(s\ge 1\), \(s\ge r\). More precisely, we prove that the uniqueness property based on a decay requirement at three times can not be lowered to two times even by imposing stronger decay on the initial data.

Keywords

Benjamin–Ono equation Weighted Sobolev space 

Notes

Acknowledgments

The author would like to thank Gustavo Ponce for prolific conversations and guidance concerning this paper and to the anonymous referee whose helpful suggestions improve the presentation of this work.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA

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