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:

- Dolce, M. & Grande, R.
*On the convergence rates of discrete solutions to the Wave Kinetic Equation*(2024).

arxiv:2404.14400

- 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

- 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

- 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

- Bedrossian, J., Coti Zelati, M. & Dolce, M.
*Taylor dispersion and phase mixing in the non-cutoff Boltzmann equation on the whole space*, (2022).

arXiv:2211.05079

- Dolce, M. & Drivas, T. D.
*On maximally mixed equilibria of two-dimensional perfect fluids*, Archive for Rational Mechanics and Analysis (2022).,

arXiv:2204.03587

- 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

- 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

- 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

- 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

- 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

- 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