Hamiltonian Birkhoff normal form for gravity-capillary water waves with constant vorticity: almost global existence
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 …
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 …
parity preserving Schr\" odinger equations on the one dimensional torus. We show that for …
Reducible KAM tori for the Degasperis–Procesi equation
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 …
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
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 …
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 …
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
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] …
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 …
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
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 …
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 …
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
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 …
manifold with quasi-periodic in time pseudo-differential perturbation of order less than or …