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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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https://hal.archives-ouvertes.fr/hal-01270936
Contributor : Luc Molinet <>
Submitted on : Monday, February 8, 2016 - 4:19:41 PM
Last modification on : Sunday, March 29, 2020 - 6:24:03 PM

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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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