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

Molinet, Luc; Saut, Jean-Claude; Tzvetkov, Nikolay

Molinet, Luc ; Saut, Jean-Claude ; Tzvetkov, Nikolay

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011), p. 653-676 / Harvested from Numdam

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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 $ℝ \times 𝕋$ 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.

Publié le : 2011-01-01

MR 2838395 | Zbl 1279.35079 | 1 citation dans Numdam

DOI : https://doi.org/10.1016/j.anihpc.2011.04.004

@article{AIHPC_2011__28_5_653_0,
     author = {Molinet, Luc and Saut, Jean-Claude and Tzvetkov, Nikolay},
     title = {Global well-posedness for the KP-II equation on the background of a non-localized solution},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {28},
     year = {2011},
     pages = {653-676},
     doi = {10.1016/j.anihpc.2011.04.004},
     mrnumber = {2838395},
     zbl = {1279.35079},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2011__28_5_653_0}
}

Molinet, Luc; Saut, Jean-Claude; Tzvetkov, Nikolay. Global well-posedness for the KP-II equation on the background of a non-localized solution. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) pp. 653-676. doi : 10.1016/j.anihpc.2011.04.004. http://gdmltest.u-ga.fr/item/AIHPC_2011__28_5_653_0/

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