Focusing solutions of the Vlasov-Poisson system

Katherine Zhiyuan Zhang

doi:10.3934/krm.2019051

Article Contents

2019, Volume 12, Issue 6: 1313-1327. Doi: 10.3934/krm.2019051

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Focusing solutions of the Vlasov-Poisson system

Katherine Zhiyuan Zhang

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

Received: January 31, 2019

Revised: April 30, 2019

Published: September 2019

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Abstract

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.

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Mathematics Subject Classification: 35Q83, 35B44, 35B40, 65M25.

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References

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