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 mixing to study quantitatively the following problems: long-time behavior of passive scalars, convergence to given equilibria in hydrodynamic stability problems or in kinetic theory in a weakly collisional regime.
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:
- 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 (2022).,
- Dolce, M. Stability threshold of the 2D Couette flow in a homogeneous magnetic field using symmetric variables (2023).
- Coti Zelati, M., Dolce, M. & Lo, C-C Diffusion enhancement and Taylor dispersion for rotationally symmetric flows in discs and pipes (2023).
- Bedrossian, J., Coti Zelati, M. & Dolce, M. Taylor dispersion and phase mixing in the non-cutoff Boltzmann equation on the whole space, (2022).
- Dolce, M. & Drivas, T. D. On maximally mixed equilibria of two-dimensional perfect fluids, Archive for Rational Mechanics and Analysis (2022).,
- 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).
- 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).
- 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).
- 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).
- 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).
- Dolce, M., & Donatelli, D. Artificial compressibility method for the Navier–Stokes–Maxwell–Stefan system, Journal of Dynamics and Differential Equations 33 35-62 (2021).