Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves

2023, Volume 28, Numbers 4-5, pp. 543-560

Author(s): Berti M., Maspero A., Murgante F.

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

Citation: Berti M., Maspero A., Murgante F., Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves, Regular and Chaotic Dynamics, 2023, Volume 28, Numbers 4-5, pp. 543-560

DOI: 10.1134/S1560354723040032

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