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CONCENTRATING SOLUTIONS OF THE RELATIVISTIC VLASOV-MAXWELL SYSTEM

Journal article
Authors J. Ben-Artzi
Simone Calogero
S. Pankavich
Published in Communications in Mathematical Sciences
Volume 17
Issue 2
Pages 377-392
ISSN 1539-6746
Publication year 2019
Published at Department of Mathematical Sciences
Pages 377-392
Language en
Links dx.doi.org/10.4310/CMS.2019.v17.n2....
Keywords Kinetic Theory, Vlasov-Maxwell, spherical symmetry, charge density, electric field, time behavior, plasma, decay, Mathematics
Subject categories Mathematics

Abstract

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.

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