Workshop: Almost global existence of periodic water waves, Massimiliano Berti

Date: 2023-09-13

Time: 10:30 - 11:20


Massimiliano Berti, SISSA


We prove an almost global in time existence result of small amplitude space periodic solutions of the 1D gravity-capillary water waves equations with constant vorticity. The result holds for any value of gravity, vorticity and depth and any surface tension belonging to a full measure set. The proof demands a Hamiltonian paradifferential Birkhoff normal form reduction for quasi-linear PDEs in presence of resonant wave interactions.