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) no. 5, pp. 653-676
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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 and perturbations that are square integrable in . In both cases we prove the global well-posedness of the Cauchy problem associated with such initial data.
@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},
pages = {653--676},
publisher = {Elsevier},
volume = {28},
number = {5},
year = {2011},
doi = {10.1016/j.anihpc.2011.04.004},
mrnumber = {2838395},
zbl = {1279.35079},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.04.004/}
}
TY - JOUR AU - Molinet, Luc AU - Saut, Jean-Claude AU - Tzvetkov, Nikolay TI - Global well-posedness for the KP-II equation on the background of a non-localized solution JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 653 EP - 676 VL - 28 IS - 5 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.04.004/ DO - 10.1016/j.anihpc.2011.04.004 LA - en ID - AIHPC_2011__28_5_653_0 ER -
%0 Journal Article %A Molinet, Luc %A Saut, Jean-Claude %A Tzvetkov, Nikolay %T Global well-posedness for the KP-II equation on the background of a non-localized solution %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %P 653-676 %V 28 %N 5 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.04.004/ %R 10.1016/j.anihpc.2011.04.004 %G en %F 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) no. 5, pp. 653-676. doi: 10.1016/j.anihpc.2011.04.004
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