## PhD research topic - Paolo Buttà

#### Research areas

Mathematical physics

#### Keywords

Interface dynamics, stochastic PDEs, interacting particle systems, kinetic models, fluid dynamics.

#### Research topics

My research activity mainly concerns the derivation of collective and macroscopic properties of systems with many degrees of freedom, in the frame of non-equilibrium statistical mechanics, kinetic theories, and fluid mechanics. Such as:

i) long-time behavior of Hamiltonian systems with infinitely many degrees of freeedom;

ii) microscopic models of viscous friction;

iii) sharp interface limit of systems undergoing a first order phase transition which are modeled as stochastic perturbations of local mean-field evolutionary equations;

iv) macroscopic description of incompressible fluids with concentrated vorticity;

v) kinetic models of self-propelled particles.

#### Bibliography

[1] P. Buttà, E. Caglioti, S. Di Ruzza, C. Marchioro, On the propagation of a perturbation in an anharmonic system, J. Stat. Phys. 127 (2007), 313-325.

[2] P. Buttà, G. Cavallaro, C. Marchioro: Mathematical models of viscous friction. Lecture Notes in Mathematics 2135, Springer (2015).

[3] L. Bertini, P. Buttà, A. Pisante, Stochastic Allen-Cahn approximation of the mean curvature flow: large deviations upper bound, Arch. Ration. Mech. Anal. 224 (2017), 659-707.

[4] P. Buttà, C. Marchioro, Long time evolution of concentrated Euler flows with planar symmetry, SIAM J. Math. Anal. 50 (2018), 735-760.