118 citations · 271 across the 30 of their papers we have counts for
6 papers · 1 filter
Time Quasi-Periodic Traveling Gravity Water Waves in Infinite Depth
Roberto Feola, Filippo Giuliani
We present the recent result [8] concerning the existence of quasi-periodic in time traveling waves for the 2d pure gravity water waves system in infinite depth. We provide the fir…
Long-time existence for semi-linear beam equations on irrational tori
Joackim Bernier, Roberto Feola, Benoît Grébert +1
We consider the semi-linear beam equation on the d dimensional irrational torus with smooth nonlinearity of order n -- 1 with n 3 and d 2. If 1 is the size of…
Long time solutions for quasi-linear Hamiltonian perturbations of Schrödinger and Klein-Gordon equations on tori
Roberto Feola, Benoît Grébert, Felice Iandoli
We consider quasi-linear, Hamiltonian perturbations of the cubic Schrödinger and of the cubic (derivative) Klein-Gordon equations on the dimensional torus. If …
Quasi-periodic traveling waves on an infinitely deep fluid under gravity
Roberto Feola, Filippo Giuliani
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, q…
A non-linear Egorov theorem and Poincaré-Birkhoff normal forms for quasi-linear pdes on the circle
Roberto Feola, Felice Iandoli
In this paper we consider an abstract class of quasi-linear para-differential equations on the circle. For each equation in the class we prove the existence of a change of coordina…
Local well-posedness for the quasi-linear Hamiltonian Schrödinger equation on tori
Roberto Feola, Felice Iandoli
We prove a local in time well-posedness result for quasi-linear Hamiltonian Schrödinger equations on for any . For any initial condition in the Sobolev spac…