118 citations · 271 across the 30 of their papers we have counts for
36 papers
Long-wave instability of periodic shear flows with constant magnetic field for the 2D resistive MHD equations
Roberto Feola, Luca Franzoi, Riccardo Montalto +1
We investigate the long-wave linear stability and instability of the two-dimensional viscous, resistive Magnetohydrodynamic (MHD) equations, in vorticity-current formulation, on th…
Quasi-resonant normal form and quadratic lifespan for 3D gravity-capillary water waves
Roberto Feola, Riccardo Montalto, Federico Murgante
We study the long-time dynamics of small-amplitude solutions to the three-dimensional gravity-capillary water waves equations for an inviscid and irrotational fluid with periodic b…
Long time dynamics close to large amplitude quasi-periodic traveling waves in two dimensional forced rotating fluids
Roberto Feola, Luca Franzoi, Riccardo Montalto
In this paper we consider the -plane equation with a smooth external force which is a quasi-periodic traveling wave of large amplitude , , and with large…
Time Quasi-Periodic Three-dimensional Traveling Gravity Water Waves
Roberto Feola, Riccardo Montalto, Shulamit Terracina
Starting with the pioneering computations of Stokes in 1847, the search of traveling waves in fluid mechanics has always been a fundamental topic, since they can be seen as buildin…
Non-resonant conditions for the Klein-Gordon equation on the circle
Roberto Feola, Jessica Elisa Massetti
We consider the infinite dimensional vector of frequencies , arising form a linear Klein-Gordon equation on the one dimensional…
Reducibility of Klein-Gordon equations with maximal order perturbations
Massimiliano Berti, Roberto Feola, Michela Procesi +1
We prove that all the solutions of a quasi-periodically forced linear Klein-Gordon equation where $ Q(ωt) := a^{(2)}(ωt, x) \partial_{xx} + a^…
Local well posedness for a system of quasilinear pdes modelling suspension bridges
Roberto Feola, Filippo Giuliani, Felice Iandoli +1
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 con…
On the lifespan of solutions and control of high Sobolev norms for the completely resonant NLS on tori
Roberto Feola, Jessica Elisa Massetti
We consider a completely resonant nonlinear Schrödinger equation on the -dimensional torus, for any , with polynomial nonlinearity of any degree , , which…
Almost global existence for some Hamiltonian PDEs with small Cauchy data on general tori
Dario Bambusi, Roberto Feola, Riccardo Montalto
In this paper we prove a result of almost global existence for some abstract nonlinear PDEs on flat tori and apply it to some concrete equations, namely a nonlinear Schrödinger equ…
Sub-exponential stability for the Beam equation
Roberto Feola, Jessica Elisa Massetti
We consider a one-parameter family of beam equations with Hamiltonian non-linearity in one space dimension under periodic boundary conditions. In a unified functional framework we…
Long time NLS approximation for the quasilinear Klein-Gordon equation on large domains under periodic boundary conditions
Roberto Feola, Filippo Giuliani
We provide the rigorous justification of the NLS approximation, in Sobolev regularity, for a class of quasilinear Hamiltonian Klein Gordon equations with quadratic nonlinearities o…
Long-time stability of the quantum hydrodynamic system on irrational tori
Roberto Feola, Felice Iandoli, Federico Murgante
We consider the quantum hydrodynamic system on a -dimensional irrational torus with . We discuss the behaviour, over a "non trivial" time interval, of the -Sobolev n…
Quadratic lifespan and growth of Sobolev norms for derivative Schrödinger equations on generic tori
Roberto Feola, Riccardo Montalto
We consider a family of Schrödinger equations with unbounded Hamiltonian quadratic nonlinearities on a generic tori of dimension . We study the behaviour of high Sobolev no…
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…
Reducibility of Schrödinger equation on a Zoll manifold with unbounded potential
Roberto Feola, Benoît Grébert, Trung Nguyen
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 or…
Reducibility of Schrödinger equation on the sphere
Roberto Feola, Benoît Grébert
In this article we prove a reducibility result for the linear Schrödinger equation on the sphere with quasi-periodic in time perturbation. Our result includes the…
Quadratic life span of periodic gravity-capillary water waves
Massimiliano Berti, Roberto Feola, Luca Franzoi
We consider the gravity-capillary water waves equations for a bi-dimensional fluid with a periodic one-dimensional free surface. We prove a rigorous reduction of this system to Bir…
Reducible KAM tori for Degasperis-Procesi equation
Roberto Feola, Filippo Giuliani, Michela Procesi
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 strategy…
Birkhoff normal form and long time existence for periodic gravity water waves
Massimiliano Berti, Roberto Feola, Fabio Pusateri
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth, and prove a rigorous reduction of these equations to Birkhoff normal form up…