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Concentrating solutions of the relativistic Vlasov-Maxwell system

Ben-Artzi, Jonathan, Calogero, Simone and Pankavich, Stephen 2019. Concentrating solutions of the relativistic Vlasov-Maxwell system. Communications in Mathematical Sciences 17 (2) , pp. 377-392. 10.4310/CMS.2019.v17.n2.a4

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We study smooth, global-in-time, spherically-symmetric solutions of the relativistic Vlasov–Poisson system that possess arbitrarily large charge densities and electric fields. In particular, we construct solutions that describe a thin shell of equally charged particles concentrating arbitrarily close to the origin and which give rise to charge densities and electric fields as large as one desires at some finite time. We show that these solutions exist even for arbitrarily small initial data or any desired mass. In the latter case, the time at which solutions concentrate can also be made arbitrarily large. As the constructed solutions are spherically-symmetric, they also satisfy the relativistic Vlasov–Maxwell system and thus our results apply to the latter system as well.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Mathematics
Publisher: International Press
ISSN: 1539-6746
Funders: EPSRC
Date of First Compliant Deposit: 9 July 2019
Date of Acceptance: 6 December 2018
Last Modified: 10 Mar 2020 23:37

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