Remarks on the Large data global solutions of $3D$ RVP system and $3D$ RVM system

TL;DR

This paper proves the global existence of solutions for a simplified 3D relativistic Vlasov-Maxwell system without magnetic fields for large cylindrically symmetric initial data, extending previous results on related systems.

Contribution

It establishes global solutions for the simplified 3D relativistic Vlasov-Maxwell system without magnetic fields, removing the vanishing order condition required in earlier work on the Vlasov-Poisson system.

Findings

Global solutions exist for large cylindrically symmetric initial data.

No vanishing order condition is needed for the simplified system.

Extends understanding of large data solutions in relativistic plasma models.

Abstract

We show that the simplified $3D$ relativistic Vlasov-Maxwell (sRVM) system, in which there is no magnetic field, poses a global solution for a class of arbitrarily large cylindrically symmetric initial data. In particular, a vanishing order condition imposed on the initial data for the relativistic Vlasov-Poisson system (RVP) in Wang(2022) is not imposed for the sRVM system.