@article {2021,
	title = {Traveling Quasi-periodic Water Waves with Constant Vorticity},
	volume = {240},
	year = {2021},
	month = {2021/04/01},
	pages = {99 - 202},
	abstract = {<p>We prove the first bifurcation result of time quasi-periodic traveling wave solutions for space periodic water waves with vorticity. In particular, we prove the existence of small amplitude time quasi-periodic solutions of the gravity-capillary water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space-periodic free interface. These quasi-periodic solutions exist for all the values of depth, gravity and vorticity, and restrict the surface tension to a Borel set of asymptotically full Lebesgue measure.</p>},
	isbn = {1432-0673},
	url = {https://doi.org/10.1007/s00205-021-01607-w},
	author = {Massimiliano Berti and Luca Franzoi and Alberto Maspero}
}
@article {2017,
	title = {Time quasi-periodic gravity water waves in finite depth},
	number = {arXiv;1708.01517},
	year = {2017},
	abstract = {We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments.},
	url = {http://preprints.sissa.it/handle/1963/35296},
	author = {P Baldi and Massimiliano Berti and Emanuele Haus and Riccardo Montalto}
}
