Research

My research is primarily centered around the aspects of fluid dynamics, with a particular emphasis on the Navier-Stokes equations, the transport equation, and the transport diffusion equation. Currently, my work is dedicated to investigating phenomena induced by mixing such as anomalous dissipation, enhanced dissipation, and the absence of selection due to vanishing viscosity.

Accepted papers:

[1] M. Colombo, L. De Rosa and M.S.: Typicality results for weak solutions of the incompressible Navier-Stokes equations. ESAIM Control Optim. Calc. Var. 28 (2022), Paper No. 38, 24. MR4438714 https://arxiv.org/abs/2102.03244
[2] V. Giri and M.S.: Non-uniqueness of integral curves for autonomous Hamiltonian vector fields. Differential Integral Equations 35 (2022), no. 7-8, 411-436. MR4412812 https://arxiv.org/abs/2108.05050
[3] M.S. and Riccardo Tione: The four-state problem and convex integration for linear differential operators. Journal of Functional Analysis, Volume 284, Issue 4, (2023). https://arxiv.org/abs/2107.10785
[4] E. Bruè, M. Colombo, G. Crippa, C. De Lellis and M.S.: Onsager critical solutions of the forced Navier–Stokes equations. Communications on Pure and Applied Analysis, 1534-0392, (2023). https://arxiv.org/abs/2212.08413
[5] J. Pitcho and M.S.: Almost everywhere non-uniqueness of integral curves for divergence-free Sobolev vector fields. SIAM Journal on Mathematical Analysis 55 (2023), pp. 4640–4663. https://arxiv.org/abs/2108.03194
[6] M. Colombo, G. Crippa and M.S.: Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence. Ann. PDE 9 (2023). https://doi.org/10.1007/s40818-023-00162-9 https://arxiv.org/06833.pdf

Submitted papers

[7] C.J.P. Johansson and M.S.: Nontrivial absolutely continuous part of anomalous dissipation measure in time. https://arxiv.org/abs/2303.09486
[8] M. Dolce, C.J.P. Johansson and M.S.: Dissipation enhancing properties for a class of Hamiltonian flows with closed streamlines. https://arxiv.org/abs/2407.06884
[9] C.J.P. Johansson and M.S.: Anomalous dissipation via spontaneous stochasticity with a two-dimensional autonomous velocity field. https://arxiv.org/abs/2409.03599
[10] T. Mörschell and M.S.: Non-uniqueness of parabolic solutions for advection-diffusion equation. https://arxiv.org/abs/2410.03308
[11] M. Inversi and M.S.: The helicity distribution for the incompressible Euler equations on bounded domains. https://arxiv.org/abs/2410.02728