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A01=Filippo Giuliani
A01=Roberto Feola
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Author_Filippo Giuliani
Author_Roberto Feola
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Quasi-Periodic Traveling Waves on an Infinitely Deep Perfect Fluid Under Gravity

English

By (author): Filippo Giuliani Roberto Feola

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. See more
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A01=Filippo GiulianiA01=Roberto FeolaAge Group_UncategorizedAuthor_Filippo GiulianiAuthor_Roberto Feolaautomatic-updateCategory1=Non-FictionCategory=PBKJCategory=PHUCOP=United StatesDelivery_Delivery within 10-20 working daysLanguage_EnglishPA=AvailablePrice_€50 to €100PS=Activesoftlaunch
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Product Details
  • Weight: 272g
  • Dimensions: 178 x 254mm
  • Publication Date: 31 May 2024
  • Publisher: American Mathematical Society
  • Publication City/Country: United States
  • Language: English
  • ISBN13: 9781470468774

About Filippo GiulianiRoberto Feola

Roberto Feola Universita degli Studi Romatre Rome Italy.Filippo Giuliani Politecnico di Milano Italy.

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