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Quasi-periodic traveling waves on an infinitely deep perfect fluid under gravity / Roberto Feola, Filippo Giuliani

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 295, number 1471 (March 2024)Publisher: Providence, RI : American Mathematical Society, March 2024Description: v, 158 SeitenISBN:
  • 9781470468774
Subject(s): Additional physical formats: 9781470477714 | Erscheint auch als: Quasi-periodic traveling waves on an infinitely deep perfect fluid under gravity. Online-Ausgabe Providence, RI : American Mathematical Society, 2024. 1 Online-Ressource (v, 158 Seiten)DDC classification:
  • 532/.0593 23/eng20240812
MSC: MSC: 76B15 | 37K55 | 37C55 | 35S05 | 76B15LOC classification:
  • QA927
Summary: 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.PPN: PPN: 1891801899
Holdings
Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-295.2024,1471 Nicht ausleihbar
Total holds: 0
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