Research

My research interests are focused on problems related to fluid dynamics and kinetic theory. Specifically, I am currently working on the dissipation enhancement generated by a general Hamiltonian flow in the advection-diffusion equation. I am also working on the description of the dynamics of vortex pairs in the 2D Navier-Stokes equations and in transition threshold problems in fluids and kinetic equations.

You can find my PhD thesis here, whose title is "Linear stability analysis of stationary Euler flows for passive scalars and inhomogeneous fluids".

Here is a list of my papers:

  1. Dolce, M. & Gallay, T. The long way of a viscous vortex dipole (2024).
    arXiv:2407.13562
  2. Dolce, M., Johansson, C.J.P., Sorella, M. Dissipation enhancing properties for a class of Hamiltonian flows with closed streamlines (2024).
    arXiv:2407.06884
  3. Dolce, M. & Grande, R. On the convergence rates of discrete solutions to the Wave Kinetic Equation, Mathematics in Engineering 6, 4 (2024).
    arxiv:2404.14400
  4. Bianchini, R., Coti Zelati, M. & Dolce, M. Symmetrization and asymptotic stability in non-homogeneous fluids around stratified shear flows, Séminaire Laurent Schwartz — EDP et applications (2023).,
    slsedp.160
    arXiv:2309.12738
  5. Dolce, M. Stability threshold of the 2D Couette flow in a homogeneous magnetic field using symmetric variables, Communications in Mathematical Physics 405, 94 (2024).
    arXiv:2308.12589
  6. Coti Zelati, M., Dolce, M. & Lo, C-C Diffusion enhancement and Taylor dispersion for rotationally symmetric flows in discs and pipes, Journal of Mathematical Fluid Mechanics 26, 12 (2023).
    arXiv:2305.18162
  7. Bedrossian, J., Coti Zelati, M. & Dolce, M. Taylor dispersion and phase mixing in the non-cutoff Boltzmann equation on the whole space, Proceedings of the London Mathematical Society 129, 1 (2024).
    arXiv:2211.05079
  8. Dolce, M. & Drivas, T. D. On maximally mixed equilibria of two-dimensional perfect fluids, Archive for Rational Mechanics and Analysis (2022).,
    arXiv:2204.03587
  9. Bedrossian, J., Bianchini, R., Coti Zelati, M. & Dolce, M. Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations, Communications on Pure and Applied Mathematics (2022).
    arXiv:2103.13713
  10. Coti Zelati, M., Dolce, M., Feng, Y. & Mazzucato, A.L. Global Existence for the Two-dimensional Kuramoto-Sivashinsky equation with a Shear Flow, Journal of Evolution Equations 21 5079–5099 (2021).
    arXiv:2103.02971
  11. Antonelli, P., Dolce, M., & Marcati, P. Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid, Annals of PDE 7 24 (2021).
    arXiv:2101.01696
  12. Bianchini, R., Coti Zelati, M. & Dolce, M. Linear inviscid damping for shear flows near Couette in the 2D stably stratified regime, Indiana University Mathematics Journal 71, 4 1467–1504 (2022).
    arXiv:2005.09058
  13. Coti Zelati, M., & Dolce, M. Separation of time-scales in drift-diffusion equations on R2, Journal de Mathématiques Pures et Appliquées 142 58-75 (2020).
    arXiv:1907.04012
  14. Dolce, M., & Donatelli, D. Artificial compressibility method for the Navier–Stokes–Maxwell–Stefan system, Journal of Dynamics and Differential Equations 33 35-62 (2021).
    arXiv:1805.06815