# Marie Skłodowska-Curie Fellowship Success

Jonathan Ben-Artzi and Junyong Zhang have been awarded a Marie Skłodowska-Curie Fellowship which will commence on 1 July 2018 for a period of two years. Their project, entitled “Geometric Analysis of Dilute Plasmas” (GRANDPA), will focus on studying regularity theory and long-time behavior of plasmas governed by the Vlasov-Maxwell system. The abstract reads:

“The ultimate goal of this Fellowship is to understand the long time behaviour of plasmas governed by the relativistic Vlasov- Maxwell system (RVM). The main difficulty is the hyperbolic nature of Maxwell’s equations (the electromagnetic fields propagate at the speed of light): particles that travel close to the speed of light nearly interact with their own fields. It is not currently known whether particles can be accelerated to such speeds, and, if so, whether this necessarily leads to development of singularities. This is a major open problem.”

The combined expertise of Jonathan and Junyong in kinetic theory and in dispersive equations played a central role in the success of this application. The total value of the award is €195,455.

# 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.