Arbitrarily large solutions of the Vlasov--Poisson system

We study smooth, global-in-time solutions of the Vlasov--Poisson system in the plasma physical case that possess arbitrarily large charge densities and electric fields. In particular, we construct two classes of solutions with this property. The first class consists of spherically symmetric solutions that initially possess arbitrarily small density and field values but attain arbitrarily large values of these quantities at some later time. Additionally, we construct a second class of spherically symmetric solutions that possess any desired mass and attain arbitrarily large density and field values at any later prescribed time