Global well-posedness for the KP-II equation on the background of a non-localized solution

Abstract : Motivated by transverse stability issues, we address the time evolution under the KP-II flow of perturbations of a solution which does not decay in all directions, for instance the KdV-line soliton. We study two different types of perturbations : perturbations that are square integrable in R × T and perturbations that are square integrable in R 2. In both cases we prove the global well-posedness of the Cauchy problem associated with such initial data.
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Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2011, 28 (5), 〈10.1016/j.anihpc.2011.04.004〉
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https://hal.archives-ouvertes.fr/hal-01270936
Contributeur : Luc Molinet <>
Soumis le : lundi 8 février 2016 - 16:19:41
Dernière modification le : vendredi 4 mai 2018 - 01:24:21

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Luc Molinet, Jean-Claude Saut, Nikolay Tzvetkov. Global well-posedness for the KP-II equation on the background of a non-localized solution. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2011, 28 (5), 〈10.1016/j.anihpc.2011.04.004〉. 〈hal-01270936〉

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