Appears in collection : Nonlinear Waves Trimester - May Conference

We prove that the capillarity waves equation in one dimension and finite depth has solutions over time intervals of length $c_N\epsilon^{-N}$ for any $N$, if the Cauchy data are of small size $\epsilon$ and space periodic, and if the gravity, or the surface tension, is taken outside a subset of zero measure. The proof relies on normal forms and on the use of the reversibility of the equation. This is joint work with Massimiliano Berti