Solutions of the 2D Radially Symmetric Vlasov-Maxwell System with an Initial Focusing Phase

We study radially symmetric solutions to the 2D Vlasov-Maxwell system and construct solutions that initially possess arbitrarily small $C^k$ norms ($k\ge 1$) for the charge densities and the electric fields, but attain arbitrarily large $L^{\mathrm{\infty }}$ norms of them at some later time.