The IVP for the dispersion generalized Benjamin–Ono equation in weighted Sobolev spaces

Fonseca, Germán ; Linares, Felipe ; Ponce, Gustavo

Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013), p. 763-790 / Harvested from Numdam

Résumé

Nous étudions le problème de Cauchy associé à lʼéquation de Benjamin–Ono avec dispersion généralisée. Notre objectif est dʼétablir les propriétés de persistance de la solution dans des espaces de Sobolev avec poids et dʼen déduire quelques propriétés de prolongement unique pour ses solutions. En particulier, nous établirons un taux de décroissance optimal pour les solutions de ce modèle.

Abstract

We study the initial value problem associated to the dispersion generalized Benjamin–Ono equation. Our aim is to establish persistence properties of the solution flow in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model.

Détail

Publié le : 2013-01-01

MR 3103170 | Zbl 06295441

DOI : https://doi.org/10.1016/j.anihpc.2012.06.006
Classification:  35B05,  35B60

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