RESEARCH INTERESTS
Dynamics of Hamiltonian PDEs and equations from Fluid Dynamics using Normal Forms techniques;
Quasi-periodic time dependent systems with fast oscillations;
Dynamics for the water waves problem: long-time existence and quasi-periodic solutions for the constant vorticity case;
Vanishing viscosity limit for time quasi-periodic solutions to Navier-Stokes equations;
Invariant structures for Euler equations close to shear flows;
Dynamics of pairs of bidimensional vortex patches;
Self-similar break-up for a viscous fluid drop: existence of the self-similar profiles and spectral stability analysis.
PUBLICATIONS
Bianchini, R.; Franzoi, L.; Montalto, R.; Terrracina, S.: Large amplitude quasi-periodic traveling waves in two dimensional forced rotating fluids. Commun. Math. Phys. 406, 66 (2025). DOI: 10.1007/s00220-025-05247-z
Franzoi, L.; Masmoudi, N.; Montalto, R.: Space quasi-periodic steady Euler flows close to the inviscid Couette flow. Arch. Rat. Mech. Anal. 248(81), 1–79, (2024). DOI: 10.1007/s00205-024-02028-1
Franzoi, L.; Montalto, R.: Time almost-periodic solutions of the incompressible Euler equations. Mathematics in Engineering 6(3), 394-406, (2024). DOI: 10.3934/mine.2024016
Franzoi, L.; Montalto, R.: A KAM approach to the inviscid limit for the 2D Navier-Stokes equations. arXiv preprint 2022, arXiv:2207.11008. (accepted for publication on Annales Herni Poincarè)
Berti M., Franzoi L., Maspero A., Pure gravity traveling quasi-periodic water waves with constant vorticity, Comm. Pure Appl. Math. 77(2), 990–1064, (2024). DOI: https://doi.org/10.1002/cpa.22143
Franzoi, L.: Reducibility for a linear wave equation with Sobolev smooth fast driven potential. Discr. Cont. Dyn. Syst., (2023), https://doi.org/10.3934/dcds.2023047.
Berti, M.; Franzoi, L.; Maspero, A.: Traveling quasi-periodic water waves with constant vorticity, Arch. Rat. Mech. Anal. 240 (1), 99-202, 2021
Berti, M.; Feola, R.; Franzoi, L.: Quadratic life span of periodic gravity-capillary water waves, Water Waves, (2020), https://doi.org/10.1007/s42286-020-00036-8.
L. Franzoi, A. Maspero: Reducibility for a fast driven linear Klein-Gordon equation. Ann. Mat. Pur. Appl. (1932-) 198 (4), 1407-1439, 2019.