A note on KAM for gravity-capillary water waves

Montalto, Riccardo¹

¹ University of Zürich Winterthurerstrasse 190 CH-8057, Zürich Switzerland

Journées équations aux dérivées partielles (2016), Exposé no. 7, 18 p.

Résumé

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 $x$) of a $2$-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.

Détail

Publié le : 2017-02-01

DOI : 10.5802/jedp.648

Classification : 76B15, 37K55, 76D45, 37K50
Keywords: KAM for PDEs, water waves, quasi-periodic solutions.

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