Concentrating solutions of the relativistic vlasov-maxwell system
Journal article, 2019

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 nite 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. © 2019 The Author(s).

Spherical symmetry

Kinetic Theory

Electric eld


Charge density


Jonathan Ben-Artzi

Cardiff University

Simone Calogero

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

S. Pankavich

Colorado School of Mines

Communications in Mathematical Sciences

1539-6746 (ISSN)

Vol. 17 2 377-392

Subject Categories

Computational Mathematics

Other Physics Topics

Mathematical Analysis



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