872 research outputs found
The IVP for the Benjamin-Ono equation in weighted Sobolev spaces
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 , and . 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.Comment: 21 page
On the persistence properties of solutions of nonlinear dispersive equations in weighted Sobolev spaces
We study persistence properties of solutions to some canonical dispersive
models, namely the semi-linear Schr\"odinger equation, the -generalized
Korteweg-de Vries equation and the Benjamin-Ono equation, in weighted Sobolev
spaces Comment: RIMS Kokyuroku Bessatsu (RIMS Proceedings, Extra Issue
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