41 citations · 350 across the 36 of their papers we have counts for
42 papers
Global dynamics for the 1d quartic Klein-Gordon equation with an internal mode
Gong Chen, Gael Y. Diebou, Adilbek Kairzhan +1
We study a one dimensional nonlinear Klein-Gordon equation with a potential, a localized quadratic nonlinearity, and a non-localized quartic nonlinearity. We assume that the linear…
Asymptotic stability of the degree-one vortex in the abelian Yang-Mills-Higgs model
Jonas Luhrmann, José M. Palacios, Fabio Pusateri +2
We prove asymptotic stability of the degree-one vortex in the -dimensional abelian Yang-Mills-Higgs model at the self-dual coupling, for small equivariant perturbations in w…
Asymptotic stability of the degree-one vortex in the abelian Yang-Mills-Higgs model: Linear Theory
Jonas Luhrmann, José M. Palacios, Fabio Pusateri +2
We study the linearized dynamics near the degree-one vortex of the -dimensional abelian Yang-Mills-Higgs model at the self-dual coupling, restricted to equivariant perturbat…
Asymptotic stability of the degree-one vortex in the abelian Yang-Mills-Higgs model: Spectral Theory and Numerics
Jonas Luhrmann, José M. Palacios, Fabio Pusateri +2
This is the first of three papers proving asymptotic stability of the degree-one vortex under equivariant perturbations in the -dimensional abelian Yang-Mills-Higgs model at…
Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves
Michal Shavit, Fabio Pusateri, Zhou Zhang +4
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Rece…
On the wave turbulence theory of 2D gravity waves, II: propagation of randomness
Yu Deng, Alexandru Ionescu, Fabio Pusateri
This is the second part of our work initiating the rigorous study of wave turbulence for water waves equations. We combine energy estimates, normal forms, and probabilistic and com…
Linearized dynamic stability for vortices of Ginzburg-Landau evolutions
José M. Palacios, Fabio Pusateri
We consider the problem of dynamical stability for the -vortex of the Ginzburg-Landau model. Vortices are one of the main examples of topological solitons, and their dynamic sta…
Local Energy control in the presence of a zero-energy resonance
José M. Palacios, Fabio Pusateri
We consider the problem of stability and local energy decay for co-dimension one perturbations of the soliton of the cubic Klein-Gordon equation in dimensions. Our main resul…
Long time regularity for 3d gravity waves with vorticity
Daniel Ginsberg, Fabio Pusateri
We consider the Cauchy problem for the full free boundary Euler equations in d with an initial small velocity of size , in a moving domain which is initially an …
On the wave turbulence theory of 2D gravity waves, I: deterministic energy estimates
Yu Deng, Alexandru D. Ionescu, Fabio Pusateri
Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKE) for water waves models. This problem has received…
Asymptotic stability near the soliton for quartic Klein-Gordon in 1D
Adilbek Kairzhan, Fabio Pusateri
We consider the nonlinear focusing Klein-Gordon equation in dimensions and the global space-time dynamics of solutions near the unstable soliton. Our main result is a proof…
On the d cubic NLS with a non-generic potential
Gong Chen, Fabio Pusateri
We consider the cubic nonlinear Schrödinger equation with an external potential that is non-generic. Without making any parity assumption on the data, but assuming that th…
Internal mode-induced growth in d nonlinear Klein-Gordon equations
Tristan Léger, Fabio Pusateri
This note complements the paper \cite{LP} by proving a scattering statement for solutions of nonlinear Klein-Gordon equations with an internal mode in d. We show that small solu…
On d quadratic Klein-Gordon equations with a potential and symmetries
Pierre Germain, Fabio Pusateri, Katherine Zhiyuan Zhang
This paper is a continuation of a previous work Germain-Pusateri (2020) by the first two authors. We focus on dimensional quadratic Klein-Gordon equations with a potential, und…
Internal modes and radiation damping for quadratic Klein-Gordon in 3D
Tristan Léger, Fabio Pusateri
We consider Klein-Gordon equations with an external potential and a quadratic nonlinearity in space dimensions. We assume that is regular and decaying and that the (m…
Maximal Speed of Quantum Propagation
Jack Arbunich, Fabio Pusateri, Israel Michael Sigal +1
For Schroedinger equations with both time-independent and time-dependent Kato potentials, we give a simple proof of the maximal speed bound. The latter states that the probability…
Quadratic Klein-Gordon equations with a potential in one dimension
Pierre Germain, Fabio Pusateri
This paper proposes a fairly general new point of view on the question of asymptotic stability of (topological) solitons. Our approach is based on the use of the distorted Fourier…
Bilinear estimates in the presence of a large potential and a critical NLS in 3d
Fabio Pusateri, Avy Soffer
We propose an approach to nonlinear evolution equations with large and decaying external potentials that addresses the question of controlling globally-in-time the nonlinear intera…
The d nonlinear Schrödinger equation with a weighted potential
Gong Chen, Fabio Pusateri
We consider the cubic nonlinear Schrödinger equation with a large external potential with no bound states. We prove global regularity and quantitative bounds for small sol…
Long-time behaviour of time-dependent density functional theory
Fabio Pusateri, Israel Michael Sigal
The density functional theory (DFT) is a remarkably successful theory of electronic structure of matter. At the foundation of this theory lies the Kohn-Sham (KS) equation. In this…
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…
Long-time existence for multi-dimensional periodic water waves
A. D. Ionescu, F. Pusateri
We prove an extended lifespan result for the full gravity-capillary water waves system with a dimensional periodic interface: for initial data of sufficiently small size $\vare…
On the global behavior of weak null quasilinear wave equations
Yu Deng, Fabio Pusateri
We consider a class of quasilinear wave equations in space-time dimensions that satisfy the "weak null condition" as defined by Lindblad and Rodnianski \cite{LR1}, and study…
Recent advances on the global regularity for irrotational water waves
Alexandru D. Ionescu, Fabio Pusateri
We review recent progress on the long-time regularity of solutions of the Cauchy problem for the water waves equations, in two and three dimensions. We begin by introducing the fre…