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Article Dans Une Revue Annales de l'Institut Henri Poincaré C, Analyse non linéaire Année : 2011

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

Résumé

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.

Dates et versions

hal-01270936 , version 1 (08-02-2016)

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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, Analyse non linéaire, 2011, 28 (5), ⟨10.1016/j.anihpc.2011.04.004⟩. ⟨hal-01270936⟩
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