Research

Publications and Preprints (reverse chronological order)

1. Grasselli. M., Poiatti, A. (2025), Convergence to equilibrium of weak solutions to the Cahn--Hilliard equation with non-degenerate mobility and singular potential, submitted, arXiv:2510.17296.

2. Gal, C.G., Grasselli, M., Poiatti, A., Shomberg, J.L. (2025), Nonlocal coupling and mobility constraints in multi-component phase segregation: modeling, theory, and dynamics, submitted, Researchgate doi: https://doi.org/10.13140/RG.2.2.36014.98889.

3. Poiatti, A. (2025), Varifold solutions to Volume-Preserving Mean Curvature Flow: existence and weak-strong uniqueness, submitted, arXiv:2507.08783.

4. Abels, H., Poiatti, A. (2025), Weak Solutions to a Sharp Interface Model for a Two-Phase Flow of Incompressible Viscous Fluids with Different Densities, submitted, arXiv:2505.06423.

5. Elbar, C., Poiatti, A. (2025), Weak solutions and sharp interface limit of the anisotropic Cahn-Hilliard equation with disparate mobility and inhomogeneous potential, submitted, arXiv:2502.11849 .

6. Poiatti, A., Stefanelli, U. (2024), Long-Time behavior of the tangential surface Navier-Stokes equation, submitted, arXiv:2412.05902.

7. Caetano, D., Elliott, C.M., Grasselli, M., Poiatti, A. (2024), Multi-component phase separation and small deformations of a spherical biomembrane, submitted, arXiv:2410.05492.

8. Abels, H., Garcke, H., Poiatti, A. (2024), Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness, submitted, arXiv:2407.14941.  

9. 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.

10. Abels, H., Garcke, H., Poiatti, A. (2025), Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Global Well-Posedness, Calc. Var. Partial Differential Equations 64, 141, https://doi.org/10.1007/s00526-025-03001-w.  

11. Poiatti, A. (2025), The 3D strict separation property for the nonlocal Cahn-Hilliard equation with singular potential, Anal. PDE 18(1), 109-139, https://doi.org/10.2140/apde.2025.18.109.

12.  Parolini, N., Poiatti, A., Vené, J., Verani, M. (2025), Structure-preserving neural networks in data-driven rheological models, SIAM J. Sci. Comput. 47(1), C182-C206, https://doi.org/10.1137/24M163109.

13.  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, Comm. Partial Differential Equations 49(9), 832–871, https://doi.org/10.1080/03605302.2024.2401445.

14. 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.

15. Gal, C.G., Poiatti, A. (2025), Unified framework for the separation property in binary phase segregation processes with singular entropy densities, European J. Appl. Math. 36, pp. 40-67, https://doi.org/10.1017/S0956792524000196.

16. Abels, H., Garcke, H., Poiatti, A. (2024), Mathematical Analysis of a Diffuse Interface Model for Multi-Phase Flows of Incompressible Viscous Fluids with Different Densities, J. Math. Fluid Mech. 26, Paper No.29, doi: 10.1007/s00021-024-00864-5, arXiv.2308.11813.

17. 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.

18. Grasselli, M., Poiatti, A. (2024), Multi-component conserved Allen-Cahn equations, Interfaces Free Bound. 26(4), 489-541, https://doi.org/10.4171/IFB/513.

19. 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.

20. 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.

21. 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.  

22. 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. 

23. 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.

24. 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.

25. 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.

26. 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.

Reports

1. Mathematics of phase separation on evolving surfaces, with H. Abels, D. Caetano, C.M. Elliott, H. Garcke, and M. Grasselli, Oberwolfach Reports, 21(1):462-464, 2024, doi: 10.4171/OWR/2024/8 .

Reviewing activities 

Peer reviews for 

Applicable Analysis;

Applied Mathematics and Optimization;

Computer Methods in Applied Mechanics and Engineering;

Communications on Pure and Applied Analysis;

Discrete and Continuous Dynamical Systems Series B;

Discrete and Continuous Dynamical Systems Series S;

European Journal of Applied Mathematics;

   Interfaces and Free Boundaries;

   Journal of Dynamical and Control Systems;

   Journal of Evolution Equations;

Journal of Mathematical Analysis and Applications; 

Journal of Mathematical Fluid Mechanics;

Mathematical Methods in the Applied Sciences;

Mathematical Models and Methods in Applied Sciences;

Mathematische Nachrichten; 

Potential Analysis;

   Proceedings of the Royal Society A; 

SIAM Journal on Mathematical Analysis;

    Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM);

Zeitschrift für angewandte Mathematik und Physik (ZAMP).