Massimiliano Berti, Alberto Maspero, Federico Murgante, “Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves”, Regul. Chaotic Dyn., 2023, Volume 28, Issue 4-5,Pages <nobr>543

This article is cited in 2 papers

Special Issue: On the 80th birthday of professor A. Chenciner

Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves

Massimiliano Berti^a, Alberto Maspero^a, Federico Murgante^ab

^a SISSA, Via Bonomea 265, 34136 Trieste, Italy
^b Universita degli studi di Trieste, Dipartimento di Matematica e Geoscienze, Via Valerio 12/1, 34127 Trieste, Italy

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.

MSC: 76B15, 37K55, 37J40

Received: 28.02.2023
Accepted: 24.07.2023

Language: English

DOI: 10.1134/S1560354723040032