Preprints:
G. Ciampa, R Lucà, Accelerated and fast magnetic reconnection through enhanced resistive dissipation for MHD equations, arXiv:2510.06801.
V. Banica, R. Lucà, N. Tzvetkov, L. Vega, On low regularity well-posedness of the binormal flow, arXiv:2505.23284.
R. Lucà, C. Peña, On the topology of the magnetic lines of large solutions to the Magnetohydrodynamic equations in R3, arXiv:2505.09340.
R. Lucà, P. Merino, Pointwise convergence of the Klein-Gordon flow, arXiv:2402.10105.
Publications:
G. Genovese, R. Lucà, R. Montalto, Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map. EMS Surv. Math. Sci. 12 (2025), no. 1, pp. 27–69
G. Ciampa, R. Lucà, Localization of Beltrami fields: global smooth solutions and vortex reconnection for the Navier-Stokes equations, J. Funct. Analysis, 287(9), https://doi.org/10.1016/j.jfa.2024.110610.
P. Caro, G. Ciampa, R. Lucà. Magnetic Reconnection in Magnetohydrodynamics, Rev. Mat. Iberoamericana, DOI: 10.4171/rmi/1512.
V. Banica, R. Lucà, N. Tzvetkov, L. Vega, Blow-up for the 1D cubic NLS, Comm. Math. Phys., DOI: 10.1007/s00220-023-04906-3.
G. Genovese, R. Lucà, N. Tzvetkov. Transport of Gaussian measures with exponential cut-off for Hamiltonian PDEs, Journal d'Analyse Mathématique, 150, 737-787, 2023.
R. Lucà, F. Ponce-Vanegas, Convergence over fractals for the Schrödinger equation, Indiana University Mathematics Journal, 71(6), pp. 2283–2307, 2022.
G. Genovese, R. Lucà, N. Tzvetkov. Quasi-invariance of Gaussian measures for the periodic Benjamin-Ono-BBM equation, Stoch. PDE: Anal. Comp., 2022, DOI: 10.1007/s40072-022-00240-2
D. Eceizabarrena, R. Lucà. Convergence over fractals for the periodic Schrödinger, Analysis and PDEs, 15(7), 1775--1805, 2022.
G. Genovese, R. Lucà, N. Tzvetkov. Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS, J. Funct. Analysis, 282(1), 2022.
E Compaan, R Lucà, G Staffilani. Pointwise Convergence of the Schrödinger Flow, International Mathematics Research Notices, 1, 596-647, 2021.
Genovese, G., Lucà, R. Local Central Limit Theorem for a Random Walk Perturbed in One Point. Math Phys Anal Geom 22(3), 1--15, 2019.
G. Crippa, C. Schulze, R. Lucà. Polynomial mixing under a certain stationary Euler flow. Physica D: Nonlinear Phenomena, 394, 44--55, 2019.
G. Genovese, R. Lucà, D. Valeri. Invariant measures for the periodic derivative nonlinear Schrödinger equation. Math. Annalen, 374(3-4),1075--1138, 2019.
R. Lucà, K. M. Rogers. Average decay of the Fourier transform of measures with applications. J. Eur. Math. Soc. (JEMS), 21(2), 465--506, 2019.
R. Lucà, K. M. Rogers. A note on pointwise convergence for the Schrödinger equation. Math. Proc. Cambridge Philos. Soc., 166(2), 209--218, 2019.
F. Cacciafesta, P. D'Ancona, R. Lucà. A limiting absorption principle for the Helmholtz equation with variable coefficients. J. Spectr. Theory, 8(4), 1349–1392, 2018.
P. D'Ancona, R. Lucà. Stability properties of the regular set for the Navier--Stokes equation. J. Math. Fluid. Mech., 20(2), 819--852, 2018.
A. Enciso, R. Lucà, D. Peralta-Salas. Vortex reconnection in the three dimensional Navier--Stokes equations. Adv. Math., 309, 452--486, 2017.
R. Lucà, K. M. Rogers. Coherence on fractals versus pointwise convergence for the Schrödinger equation. Comm. Math. Phys., 2017, 351(1), 341--359.
P. D'Ancona, R. Lucà. On the regularity set and angular integrability for the Navier--Stokes equation. Arch. Ration. Mech. Anal. (ARMA), 221(3): 1255--1284, 2016.
G. Genovese, R. Lucà, D. Valeri. Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation. Selecta Math. New Series, 22(3), 1663--1702, 2016.
P. D'Ancona, F. Cacciafesta, R. Lucà. Helmholtz and dispersive equations with variable coefficients on exterior domains. SIAM J. Math. Anal., 48(3): 1798--1832, 2016.
F. Cacciafesta, R. Lucà. Singular integrals with angular integrability, Proc. Am. Mat. Soc., 144(8): 3413--3418, 2016.
R. Lucà. Regularity criteria with angular integrability for the Navier--Stokes equation. Nonlinear Anal., 105: 24-40, 2014.
P. D'Ancona, R. Lucà. Stein--Weiss and Caffarelli--Kohn--Nirenberg inequalities with higher angular integrability. J. Math. Anal. Appl., 388(2): 1061-1079, 2012.
Proceedings:
R. Lucà, Almost sure convergence of the cubic nonlinear Schrödinger equations on T^2, Springer INdAM Series vol. 52 "Qualitative properties of dispersive PDEs'', 61--89, 2022.
R. Lucà, Transport of Gaussian measures with exponential cut-off for Hamiltonian PDEs, Oberwolfach Report: Deterministic Dynamics and Randomness in PDE, vol 19 (2022), no. 2, pp. 1447–1450.
R Lucà. Invariant measures for the DNLS equation. Mathematics of Wave Phenomena, 235-242, 2020, DOI: 10.1007/978-3-030-47174-3.
R. Lucà: Oberwolfach Report: Gibbs Measures for Nonlinear Dispersive Equations, vol 15 (2018), no. 2, pp. 1096–1098.
R. Lucà. On the size of the regular set of suitable weak solutions of the Navier--Stokes equation. Actes de Journées EDP, 2015, DOI: 10.5802/jedp.634.
G. Genovese, R. Lucà, D. Valeri. Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation. Oberwolfach Preprints (OWP), 2015, DOI: 10.14760/OWP-2015-04.