# American Institute of Mathematical Sciences

December  2019, 12(6): 1313-1327. doi: 10.3934/krm.2019051

## Focusing solutions of the Vlasov-Poisson system

 Department of Mathematics, Brown University, 151 Thayer Street, Providence, RI 02912, USA

Received  February 2019 Revised  May 2019 Published  September 2019

We study smooth, spherically-symmetric solutions to the Vlasov-Poisson system and relativistic Vlasov-Poisson system in the plasma physical case. We construct solutions that initially possess arbitrarily small $C^k$ norms ($k \geq 1$) for the charge densities and the electric fields, but attain arbitrarily large $L^\infty$ norms of them at some later time.

Citation: Katherine Zhiyuan Zhang. Focusing solutions of the Vlasov-Poisson system. Kinetic & Related Models, 2019, 12 (6) : 1313-1327. doi: 10.3934/krm.2019051
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