bokomslag Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity
Vetenskap & teknik

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

Roberto Feola Filippo Giuliani

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  • 164 sidor
  • 2024
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 NashMoser 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.
  • Författare: Roberto Feola, Filippo Giuliani
  • Format: Pocket/Paperback
  • ISBN: 9781470468774
  • Språk: Engelska
  • Antal sidor: 164
  • Utgivningsdatum: 2024-05-31
  • Förlag: American Mathematical Society