A collisionless plasma is modeled by the Vlasov‐Maxwell system. For the relativistic Vlasov‐Maxwell system in the plane, integral representations of the electromagnetic fields are derived. Using these representations it is shown that smooth solutions can break down only if particles of the plasma approach the speed of light. These results are analogous to those of Glassey & Strauss[10] in three dimensions.
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Similar content being viewed by others Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. Author information Authors and AffiliationsDepartment of Mathematics, Indiana University, Bloomington, Indiana, USA, , , , , , US
Robert T. Glassey
Department of Mathematics, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA, , , , , , US
Jack Schaeffer
(Accepted July 5, 1996)
About this article Cite this articleGlassey, R., Schaeffer, J. The Relativistic Vlasov-Maxwell System in Two Space Dimensions: Part I. Arch Rational Mech Anal 141, 331–354 (1998). https://doi.org/10.1007/s002050050079
Issue Date: April 1998
DOI: https://doi.org/10.1007/s002050050079
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