Solutions of the 2D radially symmetric Vlasov-Maxwell system with an initial focusing phase

Katherine Zhiyuan Zhang

doi:10.3934/krm.2023011

Article Contents

2023, Volume 16, Issue 6: 871-883. Doi: 10.3934/krm.2023011

This issue Previous Article Reproducing kernel Hilbert spaces in the mean field limit Next Article The mean-field limit for particle systems with uniform full-rank constraints

Solutions of the 2D radially symmetric Vlasov-Maxwell system with an initial focusing phase

Katherine Zhiyuan Zhang

Courant Institute of Mathematical Sciences, New York University, USA

Received: June 2022

Revised: March 2023

Early access: March 2023

Published: December 2023

The author is supported by an AMS-Simons travel grant

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Abstract

We study radially symmetric solutions to the 2D Vlasov-Maxwell system and 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. The proof is done by carefully tracking the trajectories of the particles to observe the emergence of a concentrating behavior. It is the first result to discuss this kind of behavior happening in the Vlasov-Maxwell dynamics.

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Mathematics Subject Classification: Primary: 35Q83, 35B44; Secondary: 35B40, 82D10.

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References

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