We present the result and the ideas of the recent paper [8] (obtained in collaboration with M. Berti) concerning the existence of Cantor families of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable ) of a -dimensional ocean, with infinite depth, in irrotational regime, under the action of gravity and surface tension at the free boundary. These quasi-periodic solutions are linearly stable.
Keywords: KAM for PDEs, water waves, quasi-periodic solutions.
@article{JEDP_2016____A7_0,
author = {Montalto, Riccardo},
title = {A note on {KAM} for gravity-capillary water waves},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
note = {talk:7},
pages = {1--18},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2016},
doi = {10.5802/jedp.648},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.648/}
}
TY - JOUR AU - Montalto, Riccardo TI - A note on KAM for gravity-capillary water waves JO - Journées équations aux dérivées partielles N1 - talk:7 PY - 2016 SP - 1 EP - 18 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.648/ DO - 10.5802/jedp.648 LA - en ID - JEDP_2016____A7_0 ER -
%0 Journal Article %A Montalto, Riccardo %T A note on KAM for gravity-capillary water waves %J Journées équations aux dérivées partielles %Z talk:7 %D 2016 %P 1-18 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.648/ %R 10.5802/jedp.648 %G en %F JEDP_2016____A7_0
Montalto, Riccardo. A note on KAM for gravity-capillary water waves. Journées équations aux dérivées partielles (2016), Talk no. 7, 18 p. doi : 10.5802/jedp.648. http://www.numdam.org/articles/10.5802/jedp.648/
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