Hamiltonian Birkhoff normal form for gravity-capillary water waves with constant vorticity: almost global existence

M Berti, A Maspero, F Murgante - Annals of PDE, 2024 - Springer
We prove an almost global existence result for space periodic solutions of the 1D gravity-
capillary water waves equations with constant vorticity. The result holds for any value of …

Long time existence for fully nonlinear NLS with small Cauchy data on the circle

R Feola, F Iandoli - arXiv preprint arXiv:1806.03437, 2018 - arxiv.org
In this paper we prove long time existence for a large class of fully nonlinear, reversible and
parity preserving Schr\" odinger equations on the one dimensional torus. We show that for …

Reducible KAM tori for the Degasperis–Procesi equation

R Feola, F Giuliani, M Procesi - Communications in mathematical physics, 2020 - Springer
We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian
perturbations of the dispersive Degasperis–Procesi equation on the circle. The overall …

Long time solutions for quasilinear Hamiltonian perturbations of Schrödinger and Klein–Gordon equations on tori

R Feola, B Grébert, F Iandoli - Analysis & PDE, 2023 - msp.org
We consider quasilinear, Hamiltonian perturbations of the cubic Schrödinger and of the
cubic (derivative) Klein–Gordon equations on the d-dimensional torus. If 𝜖≪ 1 is the size of …

Quasi-periodic traveling waves on an infinitely deep fluid under gravity

R Feola, F Giuliani - arXiv preprint arXiv:2005.08280, 2020 - arxiv.org
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, quasi …

Birkhoff normal form and long time existence for periodic gravity water waves

M Berti, R Feola, F Pusateri - Communications on Pure and …, 2023 - Wiley Online Library
We consider the gravity water waves system with a periodic one‐dimensional interface in
infinite depth and give a rigorous proof of a conjecture of Dyachenko‐Zakharov [16] …

Quadratic lifespan and growth of Sobolev norms for derivative Schrödinger equations on generic tori

R Feola, R Montalto - Journal of Differential Equations, 2022 - Elsevier
We consider a family of Schrödinger equations with unbounded Hamiltonian quadratic
nonlinearities on a generic tori of dimension d≥ 1. We study the behavior of high Sobolev …

Local well posedness for a system of quasilinear PDEs modelling suspension bridges

R Feola, F Giuliani, F Iandoli, JE Massetti - Nonlinear Analysis, 2024 - Elsevier
In this paper we provide a local well posedness result for a quasilinear beam-wave system
of equations on a one-dimensional spatial domain under periodic and Dirichlet boundary …

[图书][B] Quasi-periodic traveling waves on an infinitely deep perfect fluid under gravity

R Feola, F Giuliani - 2024 - books.google.com
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, quasi …

Reducibility of Schrödinger equation on a Zoll manifold with unbounded potential

R Feola, B Grébert, T Nguyen - Journal of Mathematical Physics, 2020 - pubs.aip.org
In this article, we prove a reducibility result for the linear Schrödinger equation on a Zoll
manifold with quasi-periodic in time pseudo-differential perturbation of order less than or …