Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity

Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity
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Publisher : Ams American Mathematical Society
Total Pages : 0
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ISBN-10 : 1470477718
ISBN-13 : 9781470477714
Rating : 4/5 (714 Downloads)

Book Synopsis Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity by : Roberto Feola

Download or read book Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity written by Roberto Feola and published by Ams American Mathematical Society. This book was released on 2024-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the first existence result of quasi-periodic water waves solutions bifurcating from a completely resonant elliptic fixed point. The proof is based on a Nash-Moser scheme, Birkhoff normal form methods and pseudo differential calculus techniques. We deal with the combined problems of small divisors and the fully-nonlinear nature of the equations. The lack of parameters, like the capillarity or the depth of the ocean, demands a refined nonlinear bifurcation analysis involving several nontrivial resonant wave interactions, as the well-known “Benjamin-Feir resonances”. We develop a novel normal form approach to deal with that. Moreover, by making full use of the Hamiltonian structure, we are able to provide the existence of a wide class of solutions which are free from restrictions of parity in the time and space variables.


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