Classical solvability of the relativistic Vlasov-Maxwell system with bounded spatial density

Abstract

In (Arch. Rational. Mech. Anal 1986, 92:59-90), Glassey and Strauss showed that if the growth in the momentum of the particles is controlled, then the relativistic Vlasov-Maxwell system has a classical solution globally in time. Later they proved that such control is achieved if the kinetic energy density of the particles remains bounded for all time (Math. Meth. Appl. Sci. 1987, 9:46-52). Here, we show that the latter assumption can be weakened to the boundedness of the spatial density.

AMS-LaTeX, 9 pages

References in corpus (2)

• On classical solutions to the 3D relativistic Vlasov-Maxwell system: Glassey-Strauss' theorem revisited
• Global classical solutions to the 3D Nordström-Vlasov system

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• A new continuation criterion for the relativistic Vlasov-Maxwell system
• On the 3D Relativistic Vlasov-Maxwell System with large Maxwell field
• Propagation of regularity and long time behavior of $3D$ massive relativistic transport equation I: Vlasov-Nordström system
• A particle approximation for the relativistic Vlasov-Maxwell dynamics
• Global solution of the $3D$ relativistic Vlasov-Maxwell system for the large radial data