[CvGmt News] Seminario E. Haus (23/01/2018)

[Alfonso Sorrentino]

SEMINARIO DI EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Universita' degli Studi di Roma "Tor Vergata"


Martedi' 23 Gennaio 2018, ore 14:30 Aula Dal Passo

Emanuele Haus (Universita' degli Studi di Napoli Federico II)

Titolo: Time quasi-periodic gravity water waves in finite depth

Abstract: We prove the existence and the linear stability of Cantor
families of small amplitude time quasi-periodic standing water wave
solutions - i.e. 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. To overcome these problems, we first reduce 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 that
requires very weak Melnikov non-resonance conditions (which lose
derivatives both in time and space), which we are able to verify for most
values of the depth parameter using degenerate KAM theory arguments. This
is a joint work with P. Baldi, M. Berti and R. Montalto.


Website: http://www.mat.uniroma2.it/~sorrenti/SeminarioED.html






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