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) no. 5, pp. 763-790.

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.

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.

Classification : 35B05, 35B60
Mots clés : Benjamin–Ono equation, Weighted Sobolev spaces

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