Mathematical Physics Seminar
On a deterministic approach to the Vlasov limit for point particles with unregularized Coulomb/Newton interactions
Carlo Lancellotti: CUNY, Staten Island Campus (NYC)
Location: Hill 705
Date & time: Thursday, 23 March 2017 at 2:00PM - 2:11PM
I will discuss some work in progress, in collaboration with Michael Kiessling, aboutthe Vlasov limit for systems of point particles with unregularized inverse squareinteractions (both repulsive and attractive). Recently, we have been able to obtain uniform bounds (with respect to N, the number of particles) for the force acting on each particle and its time derivative, under certain assumptions about the positioning of the N particles in phase space. We have also been able to prove that these good arrangements of particle are generic, and are preserved by the dynamics at least for some time. The new N-uniform bounds are a significant step forward toward a rigorousjustification of Vlasov limit for these systems, which has been a long-standing open problem.