## PhD research topic - Guido Cavallaro

#### Research areas

Mathematical physics, Kinetic theory, Fluid mechanics

#### Keywords

Infinite dynamics, viscous friction, Vlasov equation, Stokes flow.

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Research topics

Non-equilibrium statistical mechanics

In the frame of hamiltonian systems with infinitely many degrees of freeedom, it is studied the existence and uniqueness of the dynamics of infinite many classical particles.

Kinetic theory

Investigation of microscopic models of viscous friction, in particular the asymptotic behavior of the velocity of a body immersed in a gas, which turns out to be power-law instead of exponential (as often assumed in viscous friction problems). This feature is due to the non-markovian property of the dynamics, which includes long memory effects due to recollisions. Another theme in kinetic theory concerns the Vlasov equation describing a plasma, addressing the existence and uniqueness of the solution in some physical situations: presence of external fields (magnetic, electric) possibly singular on some regions of space; mutual interaction of plasma particles of different kinds (coulomb-like or other, attractive or repulsive...); case of plasma having infinite mass; velocity distribution of plasma particles having non compact support (i.e. Maxwell-Boltzmann distribution).

Fluid mechanics

Motion of a sphere in Stokes fluid, analysis of the long time behavior of the motion which is affected by the Basset memory term, reflecting on a power-law approach to equilibrium of the velocity of the sphere.

#### Bibliography

[1] S. Caprino, C. Marchioro, M. Pulvirenti: Approach to Equilibrium in a Microscopic Model of Friction. Comm. Math. Phys. 264, 167--189 (2006).

[2] S. Wollman: Global in time solution to the three-dimensional Vlasov-Poisson system. Jour. Math. Anal. Appl. 176, 76--91 (1993).

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