Jonathan Ben-Artzi, Stephen Pankavich, Junyong Zhang
Published 2021-06-21Version 1
The global-in-time existence of classical solutions to the relativistic Vlasov-Maxwell (RVM) system in three space dimensions remains elusive after nearly four decades of mathematical research. In this note, a simplified ``toy model'' is presented and studied. This toy model retains one crucial aspect of the RVM system: the phase-space evolution of the distribution function is governed by a transport equation whose forcing term satisfies a wave equation with finite speed of propagation.
Decay and non-decay of the local energy for the wave equation in the De Sitter - Schwarzschild metric
Angular Regularity and Strichartz Estimates for the Wave Equation
Strichartz estimates and moment bounds for the relativistic Vlasov-Maxwell system I. The $2$-D and $2\frac 12$-D cases
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