Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum

We consider a system ofN hard disks in ?² in the Boltzmann-Grad limit (i.e.N → ∞,d ↘ 0,N·d → λ^?1>0, whered is the diameter of the disks). If λ is sufficiently small and if the joint distribution densities factorize at time zero, we prove that the time-evolved one-particle distribution converges for all times to the solution of the Boltzmann equation with the same initial datum.     

The Cauchy Problem for the 3-D Vlasov–Poisson System with Point Charges

In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov–Poisson system in the presence of point charges with repulsive interaction. The present analysis extends an analogous two-dimensional result (Caprino and Marchioro in Kinet. Relat. Models 3(2):241–254, 2010).     

A one dimensional Boltzmann equation with inelastic collisions

We consider the Boltzmann equation for inelastic particles on the line and prove some preliminary results on existence and uniqueness of the solutions. We also discuss some connections with another kinetic equation investigated by the same authors. Conferenza tenuta il 3 novembre 1997     

Time evolution of infinite one-dimensional Coulomb system

We consider one-dimensional Coulomb systems and their time evolution given by the Newton law. We give existence and uniqueness theorems for the solutions of the equations governing the systems in the thermodynamic limits.Partially supported by the Italian C.N.R. and by the I.H.E.S.     

Time evolution of a quantum lattice system

It is shown that for a quantum lattice system associated with a Hamiltonian with a kinetic part and a potential sufficiently decreasing in the particle number, the time evolution can be described, under certain assumptions, by automorphisms of a suitable algebra.     

Controlli lineari negli spazi di Orlicz

Lavoro eseguito nell'ambito dell'attività dei Gruppi di ricerca matematica del C.N.R. I paragrafi 1 e 3 sono dovuti aG. Pulvirenti, il paragrafo 2 è dovuto aG. Santagati     

Velocity of a perturbation in infinite lattice systems

The problem of defining and estimating the velocity of disturbances in a crystal is investigated. Some results are given for plane rotors and anharmonic systems.Research partially supported by CNR.     

Generation of vorticity near the boundary in planar Navier-Stokes flows

We construct the solutions of the planar Navier-Stokes flow for a viscous incompressible fluid in the half-plane, by means of a boundary layer equation describing the production of vorticity on the boundary. Regularity properties are also discussed.Research partially supported by Ministero della Pubblica Istruzione and CNR-GNFM