New paper: Arbitrarily Large Solutions of the Vlasov-Poisson System

Jonathan Ben-Artzi recently uploaded a new paper entitled Arbitrarily large solutions of the Vlasov-Poisson system, co-authored with Stephen Pankavich and Simone Calogero.

The Vlasov-Poisson system, which models the statistical behavior of many-particle systems, is known to have global-in-time classical solutions (in three dimensions). However, the underlying particle systems (of attractive or repulsive particles) may have singularities appearing in finite time. For instance, attractive particles (stars) can collapse to a single point in finite time. It is therefore interesting to ask how close to a singularity can the Vlasov-Poisson system get?

This has recently been done by Rein & Taegert in the attractive case, however the repulsive case remained open. The main result states that for any constants C_1,C_2>0 there exists initial data with density whose L^\infty norm is initially bounded by C_1 but that at some later time T>0 is greater than C_2 . The main tool is obtaining a priori estimates for particle trajectories and choosing initial data carefully. This data is chosen to be supported on a spherical shell about the origin, with initial velocities pointing inwards.

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