Mathematics

The talk will focus on an almost global in time existence result of space periodic solutions of the gravity-capillary water waves equations with constant vorticity. These results have been recently achieved in collaboration with A. Maspero and M. Berti.

The proof demands a Hamiltonian paradifferential Birkhoff normal form reduction for quasi-linear PDEs in presence of resonant wave interactions.
We will introduce the model and the derivation of the equations of motion, starting from the free boundary Euler equation. In the following, the main ideas and ingredients, for the proof of our almost global existence result, will be explained.