Hamiltonian Paradifferential Birkhoff Normal Form for Water Waves

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.

Automated summary

This article presents the almost global existence result of small amplitude space periodic solutions of the 1D gravity-capillary water waves equations with constant vorticity. The proof is based on a novel Hamiltonian paradifferential Birkhoff normal form approach for quasi-linear PDEs.