**From July 2022 I have moved to Università di Pisa. This website and the old unimi email address will no longer be maintained.**

**Research interests:**

**Stochastic PDEs in fluid dynamics**: incompressible fluid dynamics equations perturbed by noise.**Regularization by noise**: an ill-posed ordinary or partial differential equation becomes well-posed under addition of noise.**Mean field interacting diffusions**: particle systems with diffusion and mean field interaction and applications.

**Broad interests:** Stochastic partial differential equations, stochastic fluid dynamics, interacting particle systems.

**Publications:**

- M. Coghi, W. Dreyer, P.K. Friz, P. Gajewski, C. Guhlke, M. Maurelli, A McKean-Vlasov SDE and particle system with interaction from reflecting boundaries, accepted for publication on SIAM J. Math. Anal., arXiv:2102.12315 (2021).
- M. Maurelli, Non-explosion by Stratonovich noise for ODEs, Non-explosion by Stratonovich noise for ODEs, Electron. Commun. Probab. 25 (2020), no. 68, 1–10, article, arXiv.
- M. Coghi, J.-D. Deuschel, P.K. Friz, M. Maurelli, Pathwise McKean-Vlasov theory with additive noise, Ann. Appl. Probab. 30 (2020), no. 5, 2355–2392, article, arXiv.
- M. Coghi, M. Maurelli, Regularized vortex approximation for 2D Euler equations with transport noise, Stoch. Dynam. (2020), article, arXiv.
- L. Beck, F. Flandoli, M. Gubinelli, M. Maurelli, Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness, Electron. J. Probab. 24 (2019), no. 136, 1–72, article, arXiv.
- J.-D. Deuschel, P.K. Friz, M. Maurelli, M. Slowik, The enhanced Sanov theorem and propagation of chaos, Stoch. Proc. Appl. 128 (2018), no. 7, 2228–2269, article, arXiv.
- B. Gess, M. Maurelli, Well-posedness by noise for scalar conservation laws, Comm. PDEs 43 (2018), no. 12, 1702–1736, article, arXiv.
- C. Guhlke, P. Gajewski, M. Maurelli, P.K. Friz, W. Dreyer, Stochastic model for LFPelectrodes, Cont. Mech. Thermodyn. 30 (2018), no. 3, 593–628, article.
- Z. Brzezniak, F. Flandoli, M. Maurelli, Existence and uniqueness for stochastic 2D Euler flows with bounded vorticity, Arch. Ration. Mech. Anal. 221 (2016), no. 1, 107–142, article, arXiv.
- F. Flandoli, M. Maurelli, M. Neklyudov, Noise prevents infinite stretching of the passive field in a stochastic vector advection equation, J. Math. Fluid Mech. 16 (2014), no. 4, 805–822, article, arXiv.
- M. Maurelli, Wiener chaos and uniqueness for stochastic transport equation, C. R. Math. Acad. Sci. Paris 349 (2011), no. 11-12, 669–672, article.

**Preprints:**

- J. Hoeksema, T. Holding, M. Maurelli, O. Tse, Large deviations for singularly interacting diffusions, arXiv:2002.01295 (2020).
- Z. Brzezniak, M. Maurelli, Existence for stochastic 2D Euler equations with positive H^{-1} vorticity, arXiv:1906.11523 (2019).
- F. Delarue, M. Maurelli, Zero noise limit for multidimensional SDEs driven by a pointy gradient, arXiv:1909.08702 (2019).
- M. Maurelli, K. Modin, A. Schmeding, Incompressible Euler equations with stochastic forcing: a geometric approach, arXiv:1909.09982 (2019).

**PhD thesis:**

- M. Maurelli, Regularization by noise in finite dimension, 2016.