Preprints:

1. R. Lucà, P. Merino, Pointwise convergence of the Klein-Gordon flow, arXiv:2402.10105.

2. G.Genovese, R. Lucà, R. Montalto, Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map, arXiv:2312.09795.

3. G. Ciampa, R. Lucà, Localization of Beltrami fields: global smooth solutions and vortex reconnection for the Navier-Stokes equations, arXiv:2311.01369.

4. P. Caro, G. Ciampa, R. Lucà. Magnetic Reconnection in Magnetohydrodynamics, arXiv:2209.09600.

To appear:

1. R Lucà. A note on vortex reconnection for the 3d Navier–Stokes equation. To appear in Lecture Notes of the Unione Matematica Italiana.

Publications:

1. 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.

2. 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.

3. R. Lucà, F. Ponce-Vanegas, Convergence over fractals for the Schrödinger equation, Indiana University Mathematics Journal, 71(6), pp. 2283–2307, 2022.

4. 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

5. D. Eceizabarrena, R. Lucà. Convergence over fractals for the periodic Schrödinger, Analysis and PDEs, 15(7), 1775--1805, 2022. 

6. 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.

7. E Compaan, R Lucà, G Staffilani. Pointwise Convergence of the Schrödinger Flow, International Mathematics Research Notices, 1, 596-647, 2021. 

8. 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. 

9. G. Crippa, C. Schulze, R. Lucà. Polynomial mixing under a certain stationary Euler flow. Physica D: Nonlinear Phenomena, 394, 44--55, 2019.

10. G. Genovese, R. Lucà, D. Valeri. Invariant measures for the periodic derivative nonlinear Schrödinger equation. Math. Annalen, 374(3-4),1075--1138, 2019.

11. 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. 

12. R. Lucà, K. M. Rogers. A note on pointwise convergence for the Schrödinger equation. Math. Proc. Cambridge Philos. Soc., 166(2), 209--218, 2019. 

13. 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.

14. 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.

15. A. Enciso, R. Lucà, D. Peralta-Salas. Vortex reconnection in the three dimensional Navier--Stokes equations. Adv. Math., 309, 452--486, 2017.

16. R. Lucà, K. M. Rogers. Coherence on fractals versus pointwise convergence for the Schrödinger equation. Comm. Math. Phys., 2017, 351(1), 341--359. 

17. 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. 

18. 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.                                                                             

19. 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. 

20. F. Cacciafesta, R. Lucà. Singular integrals with angular integrability, Proc. Am. Mat. Soc., 144(8): 3413--3418, 2016.

21. R. Lucà. Regularity criteria with angular integrability for the Navier--Stokes equation. Nonlinear Anal., 105: 24-40, 2014. 

22. 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:

1. 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.

2. 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.

3. R. Lucà: Oberwolfach Report: Gibbs Measures for Nonlinear Dispersive Equations, vol 15 (2018), no. 2, pp. 1096–1098.

4. 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.

5. 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.

Book paragraph

1. R Lucà. Invariant measures for the DNLS equation. Mathematics of Wave Phenomena, 235-242, 2020, DOI: 10.1007/978-3-030-47174-3.