Publications

Preprints

1. G. Ciampa, G.  Crippa & S. Spirito, Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations, arXiv:2402.07622, (2024).
2. D. Donatelli, L. Pescatore & S. Spirito, Global regularity for the one-dimensional stochastic Quantum-Navier-Stokes equations, arXiv:2401.10064, (2024).

Accepted/Published

1. S. Abbate, G. Crippa & S. Spirito, Strong convergence of the vorticity and conservation of the energy for the $alpha$-Euler equations, arXiv:2306.06641, (2023). Accepted in Nonlinearity.
2. K. Koumatos, C. Lattanzio, S. Spirito & A.E. Tzavaras, Existence and uniqueness for a viscoelastic Kelvin-Voigt model with nonconvex stored energy, Journal of Hyperbolic Differential Equations, 20 (2023), 433-474.
3. L. C. Berselli & S. Spirito, Convergence of second-order in time numerical discretizations for the evolution Navier-Stokes equations, Advances in Continuous and Discrete Models, (2022), 65.
4. P. Antonelli, S. Spirito, Global existence of weak solutions to the Navier-Stokes-Korteweg equations, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, 39 (2022), 171–200.
5. P. Antonelli, G. Cianfarani Carnevale, C. Lattanzio & S. Spirito, Relaxation limit from the Quantum-Navier-Stokes equations to the Quantum Drift Diffusion equation, Journal of Nonlinear Science, 31 (2021), Paper No. 71.
6. P. Antonelli, L. E. Hientzsch & S. Spirito, Global existence of finite energy weak solutions   to the Quantum Navier-Stokes equations with non-trivial far-field behavior, Journal of Differential Equations, 290 (2021), 147-177.
7. L.C. Berselli & S. Spirito, On the Existence of Leray-Hopf Weak Solutions to the Navier- Stokes Equations, in Special Issue Teaching and Learning of Fluid Mechanics, Volume II, Fluids, 6 (1) 2021, p. 42.
8. G. Ciampa, G.  Crippa & S. Spirito, Strong convergence of the vorticity for the 2D Euler Equations in the inviscid limit, Archive for Rational Mechanics and Analysis, 240 (2021), 295-326.
9. E. Di Iorio, P. Marcati & S. Spirito, Splash singularity for a free-boundary incompressible viscoelastic fluid model, Advances in Mathematics, 368 (2020), Paper No. 107124, 64 pp.
10. E. Di Iorio, P. Marcati & S. Spirito, Splash singularities for a general Oldroyd model with finite Weissenberg number, Archive of Rational Mechanics and Analysis, 235 (2020), no. 3, 1589-1660.
11. G. Ciampa, G.  Crippa & S. Spirito, Smooth approximation is not a selection principle for the transport equation with rough vector field, Calculus of Variations and Partial Differential Equations 59 (2020), no. 1, Paper No. 13, 21 pp.
12. G. Ciampa, G.  Crippa & S. Spirito, Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy. Journal of Nonlinear Science, 30 (2020), 2787-2820.
13. G. Ciampa, G.  Crippa & S. Spirito, On smooth approximations of rough vector fields and the selection of flows. in Hyperbolic Problems: Theory, Numerics, Applications AIMS Serie Applied Mathematics, 10 (2020), 361-369.
14. K. Koumatos & S. Spirito, Quasiconvex elastodynamics: weak-strong uniqueness for measure- valued solutions, Communications on Pure Applied Mathematics, 72 (2019), no. 6, 1288-1320. Corrigendum: Communications on Pure Applied Mathematics, 73 (2020), no.10, 2284-2291.
15. L. C. Berselli, S. Fagioli & S. Spirito, Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization, Journal de Mathématiques Pures et Appliqués, 125 (2019), no. 9, 189-208.
16. P. Antonelli & S. Spirito, On the compactness of weak solutions to the Navier-Stokes- Korteweg equations for capillary fluids, Nonlinear Analysis, 187 (2019), 110-124.
17. L. C. Berselli & S. Spirito, On the convergence of a fully discrete scheme of LES type to physically relevant solutions of the incompressible Navier-Stokes, Zeitschrift für angewandte Mathematik und Physik, 69 (2018), no. 3, Art. 61, 15 pp.
18. P. Antonelli & S. Spirito, On the compactness of finite energy weak solutions to the Quantum Navier-Stokes equations, Journal of Hyperbolic Differential Equations, 15 (2018), no. 1, 133-147.
19. E. Di Iorio, P. Marcati & S. Spirito, Splash singularity for a free-boundary incompressible viscoelastic fluid model, in Proceeding of XVI International Conference on Hyperbolic Problems Theory, Numerics, Applications, Aachen (Germany), August 1-5, 2016. (2018).
20. L. C. Berselli & S. Spirito, On the construction of suitable weak solutions to the 3D Navier- Stokes equations in a bounded domain by an artificial compressibility method, Communications in Contemporary Mathematics, 20 (2018), no. 1, 1650064, 16 pp.
21. G. Crippa, N. Gusev, S. Spirito & E. Wiedemann, Failure of the chain rule for the divergence of bounded vector fields, Annali Scuola Normale Superiore Pisa Classe di Scienze (5), 17 (2017), no. 1, 1-18.
22. E. Di Iorio, P. Marcati & S. Spirito, Splash singularities for a 2D Oldroyd-B model with nonlinear Piola-Kirchhoff stress, in Hyperbolic PDEs, Fluids, Transport and Applications: Dedicated to Alberto Bressan for his 60th birthday, NoDEA - Nonlinear Differential Equations and Applications, (2017), pp.24-60.
23. P. Antonelli & S. Spirito, Global Existence of Finite Energy Weak Solutions of Quantum Navier-Stokes Equations, Archive of Rational Mechanics and Analysis, 225 (2017), no. 3, 1161-1199.
24. G. Crippa, C. Nobili, C. Seis & S. Spirito, Eulerian and Lagrangian solutions to the continuity and Euler equations with L1 vorticity, SIAM Journal of Mathematical Analysis, 49 (2017), no. 5, 3973-3998.
25. L. C. Berselli & S. Spirito, Suitable weak solutions to the 3D Navier-Stokes equations are constructed with the Voigt Approximation, Journal of Differential Equations, 262 (2017), no. 5, 3285-3316.
26. L. C. Berselli & S. Spirito, Weak solutions to the Navier-Stokes equations constructed by semi-discretization are suitable, in Recent Advances in Partial Differential Equations and Applications, 85-97, Contemporary Mathematics, 666 Amer. Math. Soc., Providence, RI, (2016).
27. G. Crippa, M. Colombo & S. Spirito, Logarithmic estimates for continuity equations, in Special issue on contemporary topics in conservation laws, Network and Heterogeneous Media, 11 (2016), no. 2, 301-311.
28. D. Donatelli & S. Spirito, Vanishing dielectric constant regime for the Navier Stokes Maxwell equations, NoDEA - Nonlinear Differential Equations and Applications, 23 (2016), no. 3, Art. 28, 19 pp.
29. M. Colombo, G. Crippa & S. Spirito, Renormalized solutions to the continuity equation with an integrable damping term, Calculus of Variations and PDE, 54 (2015), no. 2, 1831-1845.
30. G. Crippa, N. Gusev, S. Spirito E. Wiedemann, Non-uniqueness and prescribed energy for the continuity equation, Communication in Mathematical Science, 13 (2015), no. 7, 1937-1947.
31. G. Crippa & S. Spirito, Renormalized Solutions of the 2D Euler Equations. Communications in Mathematical Physics, 339 (2015), no. 1, 192-198.
32. G. Crippa, E. Semenova S. Spirito, Strong continuity for the 2D Euler equations., Kinetic and Related Models, 8 (2015), no. 4, 685-689.
33. L. C. Berselli & S. Spirito, An elementary approach to inviscid limits for the 3D Navier- Stokes equations with slip boundary conditions and applications to the 3D Boussinesq equations, NoDEA - Nonlinear Differential Equations and Applications, 21 (2014), no. 2, 149-166.
34. L. C. Berselli & S. Spirito, On inviscid limits for the Navier-Stokes equations with slip boundary conditions involving the vorticity, in Hyperbolic Problems: theory, numerics, applications, AIMS Serie Applied Mathematics, 8 (2014), 967-974.
35. L. C. Berselli & S. Spirito, On the vanishing viscosity limit for the Navier-Stokes equations under slip boundary conditions in general domains, Communications in Mathematical Physics, 316 (2012), no. 1, 171-198
36. L. C. Berselli & S. Spirito, A remark on the Euler equations in dimension two, in Proceedings of the Intensive Research Month on Hyperbolic Conservation Laws and Fluid Dynamics Parma (Italy), February 1 - 28, 2010, Rivista Matematica Università di Parma, 3 (2012), no. 1, 1-23.
37. L. C. Berselli & S. Spirito, On the Boussinesq system: regularity criteria and singular lim- its, Methods Applied Analysis, 18 (2011), no. 4, 391-416.
38. D. Donatelli & S. Spirito, Weak solutions of Navier-Stokes equations constructed by artificial compressibility method are suitable, Journal of Hyperbolic Differential Equations, 8 (2011), no. 1, 101-113.
39. S. Spirito, Solutions of the Navier-Stokes equations constructed by artificial compressibility approximation are suitable, in Proceeding of Seventh Meeting on Hyperbolic Conservation Laws and Fluid Dynamics: Recent Results and Research Perspectives Trieste (Italy), August 31 - September 4, 2009, Rivista Matematica Università di Parma, 1 (2010), no. 1, 219-230.