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 …

A Nekhoroshev theorem for some perturbations of the Benjamin-Ono equation with initial data close to finite gap tori

D Bambusi, P Gérard - Mathematische Zeitschrift, 2024 - Springer
We consider a perturbation of the Benjamin Ono equation with periodic boundary conditions
on a segment. We consider the case where the perturbation is Hamiltonian and the …

Exponential stability of solutions to the Schr {\" o} dinger-Poisson equation

J Bernier, N Camps, B Grébert, Z Wang - arXiv preprint arXiv:2310.16476, 2023 - arxiv.org
We prove an exponential stability result for the small solutions of the Schr {\" o} dinger-
Poisson equation on the circle without exterior parameters in Gevrey class. More precisely …

Globally integrable quantum systems and their perturbations

D Bambusi, B Langella - arXiv preprint arXiv:2403.18670, 2024 - arxiv.org
In this paper we present the notion of globally integrable quantum system that we introduced
in [BL22]: we motivate it using the spectral theory of pseudodifferential operators and then …

Long time stability for cubic nonlinear Schr\" odinger equations on non-rectangular flat tori

J Bernier, N Camps - arXiv preprint arXiv:2402.04122, 2024 - arxiv.org
We consider nonlinear Schr\" odinger equations on flat tori satisfying a simple and explicit
Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term …

Long time stability result for d-dimensional nonlinear Schrödinger equation

H Cong, S Li, X Wu - Journal of Differential Equations, 2024 - Elsevier
Long time stability result for d-dimensional nonlinear Schrödinger equation - ScienceDirect
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Energy cascade and Sobolev norms inflation for the quantum Euler equations on tori

F Giuliani, R Scandone - arXiv preprint arXiv:2410.21080, 2024 - arxiv.org
In this paper we prove the existence of solutions to the quantum Euler equations on
$\mathbb {T}^ d $, $ d\geqslant 2$, with almost constant mass density, displaying energy …

Almost global existence for some Hamiltonian PDEs on manifolds with globally integrable geodesic flow

D Bambusi, R Feola, B Langella, F Monzani - arXiv preprint arXiv …, 2024 - arxiv.org
In this paper we prove an abstract result of almost global existence for small and smooth
solutions of some semilinear PDEs on Riemannian manifolds with globally integrable …

Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map

G Genovese, R Lucà, R Montalto - arXiv preprint arXiv:2312.09795, 2023 - arxiv.org
arXiv:2312.09795v1 [math.AP] 15 Dec 2023 Page 1 arXiv:2312.09795v1 [math.AP] 15 Dec
2023 TRANSFORMATION OF THE GIBBS MEASURE OF THE CUBIC NLS AND FRACTIONAL …

Almost Global Existence for d-dimensional Beam Equation with Derivative Nonlinear Perturbation

X Wu, J Zhao - Qualitative Theory of Dynamical Systems, 2024 - Springer
Almost Global Existence for d-dimensional Beam Equation with Derivative Nonlinear
Perturbation | Qualitative Theory of Dynamical Systems Skip to main content SpringerLink …