Research
Research interests
Regularisation by noise in ODEs and PDEs
(Stochastic) fluid dynamics equations
Rough paths
McKean-Vlasov equations and interacting particle systems
Submitted preprints
M. Bagnara, L. Galeati, M. Maurelli. Regularization by rough Kraichnan noise for the generalised gSQG equations. https://arxiv.org/abs/2405.12181 (2024)
L. Galeati, K. Lê, A. Mayorcas. Quantitative Propagation of Chaos for Singular Interacting Particle Systems Driven by Fractional Brownian Motion. https://arxiv.org/abs/2403.05454 (2024)
L. Galeati, D. Luo. Weak well-posedness by transport noise for a class of 2D fluid dynamics equations. https://arxiv.org/abs/2305.08761 (2023)
L. Galeati, M. Gerencsér. Solution theory of fractional SDEs in complete subcritical regimes. https://arxiv.org/abs/2207.03475 (2022)
Accepted preprints
L. Galeati. A note on weak existence for singular SDEs. https://arxiv.org/abs/2309.06295 (2023). To appear on Stoch. Dyn., see here.
L. Galeati, M. Gubinelli. Prevalence of ρ-irregularity and related properties. arXiv:2004.00872 (2020). To appear on Ann. Inst. H. Poincaré Probab. Statist., see here.
Publications
F. Flandoli, L. Galeati, D. Luo. Quantitative convergence rates for scaling limit of SPDEs with transport noise. J. Diff. Equ. 394, 237-277 (2024). https://doi.org/10.1016/j.jde.2024.02.053
L. Galeati, M. Gubinelli. Mixing for generic rough shear flows. SIAM J. Math. Anal. 55(6), 7240–7272 (2023). https://doi.org/10.1137/23M155222X
L. Galeati, D. Luo. LDP and CLT for SPDEs with transport noise. Stoch PDE: Anal Comp (2023). https://doi.org/10.1007/s40072-023-00292-y
L. Galeati, C. Ling. Stability estimates for singular SDEs and applications. Electron. J. Prob. 28, 1-31(2023). https://doi.org/10.1214/23-EJP913
L. Galeati, F.A. Harang. Regularization of multiplicative SDEs through additive noise. Ann. Appl. Probab. 32(5), 3930–3963 (2022). https://doi.org/10.1214/21-AAP1778
L. Galeati, F.A. Harang, A. Mayorcas. Distribution Dependent SDEs driven by additive fractional Brownian motion. Probab. Theory Relat. Fields (2022). https://doi.org/10.1007/s00440-022-01145-w
L. Galeati, F.A. Harang, A. Mayorcas. Distribution Dependent SDEs driven by additive continuous noise. Electron. J. Prob. 27, 1–38 (2022). https://doi.org/10.1214/22-EJP756
F. Flandoli, L. Galeati, D. Luo. Eddy heat exchange at the boundary under white noise turbulence. Philos. Trans. Royal Soc. A 380, Issue 2219 (2022). https://doi.org/10.1098/rsta.2021.0096
L. Galeati, M. Gubinelli. Noiseless regularisation by noise. Rev. Mat. Iberoam. 38(2), pp. 433–502 (2022). DOI:10.4171/RMI/1280
F. Flandoli, L. Galeati, D. Luo. Delayed blow-up by transport noise. Comm. PDEs 46(9), 1757–1788 (2021). https://doi.org/10.1080/03605302.2021.1893748
L. Galeati. Nonlinear Young Differential Equations: A Review. J. Dyn. Diff. Equ. (2021). https://doi.org/10.1007/s10884-021-09952-w
F. Flandoli, L. Galeati, D. Luo. Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier–Stokes equations. J. Evol. Equ. 21, 567–600 (2021). https://doi.org/10.1007/s00028-020-00592-z
L. Galeati. On the convergence of stochastic transport equations to a deterministic parabolic one. Stoch PDE: Anal Comp 8, 833–868 (2020). https://doi.org/10.1007/s40072-019-00162-6