Publications
D. Bambusi, A. Belloni, F. Giuliani. "Non relativistic limit of the nonlinear Klein-Gordon equation: Uniform in time approximation of KAM solutions" Accepted on Archive for Rational Mechanics and Analysis (2026). https://arxiv.org/abs/2501.17691
F. Giuliani, R. Scandone. "Energy cascade and Sobolev norms inflation for the quantum Euler equations on tori." Advances in Mathematics 479 (2025), 110453. https://doi.org/10.1016/j.aim.2025.110453
R. Feola, F. Giuliani. "Long time dynamics of quasi-linear Hamiltonian Klein-Gordon equations on the circle." Journal of Dynamics and Differential Equations 37 (2025), 2003-2075. https://doi.org/10.1007/s10884-024-10365-8
F. Giuliani. "Sobolev instability in the cubic NLS equation with convolution potentials on irrational tori." Journal of Differential Equations 416 (2025), 1-27. https://arxiv.org/abs/2308.13468
P. Baldi, F. Giuliani, M. Guardia, E. Haus. "Effective chaos for the Kirchhoff equation on tori." Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire 42 (2025), no. 2, 281-330. https://doi.org/10.4171/AIHPC/110
F. Giuliani, M. Guardia. "Arnold diffusion in Hamiltonian systems on infinite lattices." Communications on Pure and Applied Mathematics 77 (2024), no. 8, 3333-3426. https://doi.org/10.1002/cpa.22191
R. Feola, F. Giuliani. "Quasi-periodic traveling waves on an infinitely deep perfect fluid under gravity." Memoirs of the American Mathematical Society 295 (2024), no. 1471, 1-158. https://doi.org/10.1090/memo/1471
R. Feola, F. Giuliani, F. Iandoli, J. E. Massetti. "Local well posedness for a system of quasilinear PDEs modelling suspension bridges." Nonlinear Analysis 240 (2024), 113442. https://doi.org/10.1016/j.na.2023.113442
F. Giuliani, M. Guardia. "Sobolev norms explosion for the cubic NLS on irrational tori." Nonlinear Analysis 220 (2022), 112865. https://doi.org/10.1016/j.na.2022.112865
F. Giuliani. "Transfers of energy through fast diffusion channels in some resonant PDEs on the circle." Discrete and Continuous Dynamical Systems - Series A 41 (2021), no. 11, 5057-5085. https://doi.org/10.3934/dcds.2021068
F. Giuliani, M. Guardia, P. Martín, S. Pasquali. "Chaotic-like transfers of energy in Hamiltonian PDEs." Communications in Mathematical Physics 384 (2021), 1227-1290. https://doi.org/10.1007/s00220-021-03956-9
F. Giuliani, M. Guardia, P. Martín, S. Pasquali. "Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs." Rendiconti Lincei. Matematica e Applicazioni 32 (2021), 149-165. https://doi.org/10.4171/RLM/931
R. Feola, F. Giuliani. "Time quasi-periodic traveling gravity water waves in infinite depth." Rendiconti Lincei. Matematica e Applicazioni 31 (2020), 901-916. https://doi.org/10.4171/RLM/919
R. Feola, F. Giuliani, M. Procesi. "Reducible KAM tori for the Degasperis-Procesi equation." Communications in Mathematical Physics 377 (2020), 1681-1759. https://doi.org/10.1007/s00220-020-03788-z
R. Feola, F. Giuliani, R. Montalto, M. Procesi. "Reducibility of first order linear operators on tori via Moser's theorem." Journal of Functional Analysis 276 (2019), no. 3, 932-970. https://doi.org/10.1016/j.jfa.2018.10.009
R. Feola, F. Giuliani, M. Procesi. "Reducibility for a class of weakly dispersive linear operators arising from the Degasperis-Procesi equation." Dynamics of Partial Differential Equations 16 (2019), no. 1, 25-94. https://doi.org/10.4310/DPDE.2019.v16.n1.a2
R. Feola, F. Giuliani, S. Pasquali. "On the integrability of Degasperis-Procesi equation: control of the Sobolev norms and Birkhoff resonances." Journal of Differential Equations 266 (2019), no. 6, 3390-3437. https://doi.org/10.1016/j.jde.2018.09.003
F. Giuliani. "Quasi-periodic solutions for quasi-linear generalized KdV equations." Journal of Differential Equations 262 (2017), no. 10, 5052-5132. https://doi.org/10.1016/j.jde.2017.01.021
Preprints
1. A. Belloni, F. Giuliani. "Global Well-Posedness and Uniform Long-Time Control for a Class of Periodic NLS-Dysthe Equations." Preprint (2026), arXiv:2610.14786. https://arxiv.org/abs/2610.14786
2. Y. Cacchiò, F. Giuliani, F. Iandoli, R. Scandone. "Long time strong Sobolev instability for quasilinear NLS." Preprint (2026), arXiv:2609.37593. https://arxiv.org/abs/2609.37593
