Time quasi-periodic gravity water waves in finite depth

@article{Baldi2018TimeQG,
  title={Time quasi-periodic gravity water waves in finite depth},
  author={Pietro Baldi and Massimiliano Berti and Emanuele Haus and Riccardo Montalto},
  journal={Inventiones mathematicae},
  year={2018},
  volume={214},
  pages={739-911}
}
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 fully nonlinear nature of the gravity water waves equations—the… CONTINUE READING
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