Open AccessA toy model for the relativistic Vlasov-Maxwell system
Author(s) -
Jonathan Ben-Artzi,
Stephen Pankavich,
Junyong Zhang
Publication year - 2022
Publication title -
kinetic and related models
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.987
H-Index - 28
eISSN - 1937-5093
pISSN - 1937-5077
DOI - 10.3934/krm.2021053
Subject(s) - vlasov equation , phase space , physics , forcing (mathematics) , space (punctuation) , term (time) , distribution (mathematics) , distribution function , function (biology) , maxwell's equations , classical mechanics , mathematical physics , mathematical analysis , statistical physics , mathematics , computer science , plasma , quantum mechanics , evolutionary biology , biology , operating system
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.