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Time quasiperiodic gravity water waves in finite depth
http://sms.cam.ac.uk/media/2579430
Baldi, P
Thursday 5th October 2017  09:00 to 09:45
40
Time quasiperiodic gravity water waves in finite depth
http://sms.cam.ac.uk/media/2579430
http://rss.sms.cam.ac.uk/itunesimage/2567247.jpg
no

Time quasiperiodic gravity water waves in finite depth
ucs_sms_2561139_2579430
http://sms.cam.ac.uk/media/2579430
Time quasiperiodic gravity water waves in finite depth
Baldi, P
Thursday 5th October 2017  09:00 to 09:45
Fri, 06 Oct 2017 09:00:01 +0100
Isaac Newton Institute
Baldi, P
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Baldi, P
Thursday 5th October 2017  09:00 to 09:45
Baldi, P
Thursday 5th October 2017  09:00 to 09:45
Cambridge University
2777
http://sms.cam.ac.uk/media/2579430
Time quasiperiodic gravity water waves in finite depth
Baldi, P
Thursday 5th October 2017  09:00 to 09:45
We consider the water wave equations for a 2D ocean of finite depth under the action of gravity. We present a recent existence and linear stability result for small amplitude standing wave solutions that are periodic in space and quasiperiodic in time. The result holds for values of a normalized depth parameter in a Cantorlike set of asymptotically full measure.
The main difficulties of the problem are the presence of derivatives in the nonlinearity (the system is quasilinear), and a small divisors problem where the frequencies of the linear part grow in a sublinear way at infinity (like the square root of integers). To overcome these problems we first reduce the linearized operators (which are obtained at each approximate quasiperiodic solution along a NashMoser iteration) to constant coefficients up to smoothing operators, using pseudodifferential changes of variables that are quasiperiodic in time. Then we apply a KAM reducibility scheme which requires very weak second Melnikov nonresonance conditions (losing derivatives both in time and space). Such nonresonance conditions are sufficiently weak to be satisfied for most values of the normalized depth parameter, thanks to arguments from degenerate KAM theory.
Joint work with Massimiliano Berti, Emanuele Haus and Riccardo Montalto.
20171006T09:00:02+01:00
2777
2579430
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