Abstract:
We present the almost global in time existence result in [13] of small amplitude
space periodic solutions of the 1D gravity-capillary water waves equations with constant vorticity
and we describe the ideas of proof. This is based on a novel Hamiltonian paradifferential Birkhoff
normal form approach for quasi-linear PDEs.
Keywords:
water waves equations, vorticity, Hamiltonian Birkhoff normal form, paradifferential
calculus.
Funding agency
Grant number
PRIN
2020XB3EFL001
Research supported by PRIN 2020 (2020XB3EFL001) ''Hamiltonian and dispersive PDEs''.
Citation:
Massimiliano Berti, Alberto Maspero, Federico Murgante, “Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves”, Regul. Chaotic Dyn., 28:4-5 (2023), 543–560
\Bibitem{BerMasMur23}
\by Massimiliano Berti, Alberto Maspero, Federico Murgante
\paper Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 4-5
\pages 543--560
\mathnet{http://mi.mathnet.ru/rcd1220}
\crossref{https://doi.org/10.1134/S1560354723040032}
Linking options:
https://www.mathnet.ru/eng/rcd1220
https://www.mathnet.ru/eng/rcd/v28/i4/p543
This publication is cited in the following 5 articles:
Massimiliano Berti, Scipio Cuccagna, Francisco Gancedo, Stefano Scrobogna, “Paralinearization and extended lifespan for solutions of the α-SQG sharp front equation”, Advances in Mathematics, 460 (2025), 110034
Lizhe Wan, “Low regularity well-posedness for two-dimensional deep gravity water waves with constant vorticity”, Communications in Partial Differential Equations, 2025, 1
Thomas Alazard, Oberwolfach Seminars, 54, Free Boundary Problems in Fluid Dynamics, 2024, 1
Riccardo Montalto, Federico Murgante, Stefano Scrobogna, “Quadratic Lifespan for the Sublinear αα-SQG Sharp Front Problem”, J Dyn Diff Equat, 2024
Massimiliano Berti, Alberto Maspero, Federico Murgante, “Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves”, Regul. Chaotic Dyn., 28:4 (2023), 543–560
Citation in format AMSBIB
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