Research

Publications and Preprints (reverse chronological order)

1. Gal, C.G., Grasselli, M., Poiatti, A., Shomberg, J.L. (2024), Multi-component Cahn-Hilliard systems with singular potentials: numerical results and cascading phenomena, submitted, Researchgate doi: http://dx.doi.org/10.13140/RG.2.2.12188.09601.

2.  Parolini, N., Poiatti, A., Vené, J., Verani, M. (2024), Structure-preserving neural networks in data-driven rheological models, submitted, arXiv:2401.07121.

3.  Hurm, C., Knopf, P., Poiatti, A. (2024), Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential, submitted, arXiv:2403.10947.

4. Elbar, C., Perthame, B., Poiatti, A., Skrzeczkowski, J. (2024), Nonlocal Cahn-Hilliard equation with degenerate mobility: Incompressible limit and convergence to stationary states, Arch. Ration. Mech. Anal., 248:41, online first, https://doi.org/10.1007/s00205-024-01990-0, arXiv.2305.06239.

5. Gal, C.G., Poiatti, A. (2023), Unified framework for the separation property in binary phase segregation processes with singular entropy densities, accepted in European J. Appl. Math., https://doi.org/10.1017/S0956792524000196.

6. Abels, H., Garcke, H., Poiatti, A. (2024), Global regularity and asymptotic stabilization for the incompressible multi-component Navier-Stokes-Cahn-Hilliard model with unmatched densities, J. Math. Fluid Mech. 26, Paper No.29, doi: 10.1007/s00021-024-00864-5, arXiv.2308.11813.

7. Poiatti, A., Signori, A. (2024), Regularity results and optimal velocity control of the convective nonlocal Cahn-Hilliard equation in 3D, ESAIM Control Optim. Calc. Var. 30, Paper No. 21, 36pp, doi.org/10.1051/cocv/2024007.

8. Grasselli, M., Poiatti, A. (2024), Multi-component conserved Allen-Cahn equations, accepted in Interfaces Free Bound., https://doi.org/10.4171/IFB/513, arXiv.2304.03363.

9. Poiatti, A. (2023), The 3D strict separation property for the nonlocal Cahn-Hilliard equation with singular potential, accepted in Anal. PDE, arXiv:2303.07745.

10. Gal, C.G., Grasselli, M., Poiatti, A. (2023), Allen-Cahn-Navier-Stokes-Voigt systems with moving contact lines, J. Math. Fluid Mech. 25, Paper No. 89, 57 pp., doi:10.1007/s00021-023-00829-0.

11. Gal, C.G., Grasselli, M., Poiatti, A., Shomberg, J.L. (2023), Multi-component Cahn-Hilliard systems with singular potentials: Theoretical results,  Appl. Math. Optim. 88(73), doi:10.1007/s00245-023-10048-8.

12. Caetano, D., Elliott, C.M., Grasselli, M., Poiatti, A. (2023), Regularisation and separation for evolving surface Cahn-Hilliard equations, SIAM J. Math. Anal. 55(6), 6625-6675, doi:10.1137/22M1497213.  

13. Grasselli, M., Poiatti, A. (2023), A phase-field model for multiscale modeling of thrombus biomechanics in blood vessels: local well-posedness in dimension two, Discrete Contin. Dyn. Syst. Ser. S 16(9), 2364-2425, doi:10.3934/dcdss.2023105. 

14. Gal, C.G., Giorgini, A., Grasselli, M., Poiatti, A. (2023), Global well-posedness and convergence to equilibrium for the Abels-Garcke-Grün model with nonlocal free energy, J. Math. Pures Appl. (9) 178, 46-109, doi:10.1016/j.matpur.2023.07.005.

15. Grasselli, M., Parolini, N., Poiatti, A., Verani, M. (2023), Non-isothermal non-Newtonian fluids: the stationary case, Math. Models Methods Appl. Sci. 33(9),1747-1801, doi:10.1142/S0218202523500410.

16. Grasselli, M., Poiatti, A. (2022) , A phase separation model for binary fluids with hereditary viscosity, Math. Methods Appl. Sci. 45(17), 11031-11066, doi:10.1002/mma.8436.

17. Grasselli, M., Poiatti, A. (2022), The Cahn-Hilliard-Boussinesq system with singular potential, Commun. Math. Sci. 20(4), 897-946, doi:10.4310/CMS.2022.v20.n4.a1.

Work in progress

1. Caetano, D., Elliott, C.M., Grasselli, M., Poiatti, A., Multi-component domain formation via phase separation for spherical biomembranes with small deformations, in preparation.

Reviewing activities 

Peer reviews for 

Discrete and Continuous Dynamical Systems Series S;

Journal of Mathematical Analysis and Applications; 

Applicable Analysis;

Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM);

Zeitschrift für angewandte Mathematik und Physik (ZAMP);

    Interfaces and Free Boundaries.