A New Continuation Criterion for the Relativistic Vlasov–Maxwell System
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The global existence of solutions to the relativistic Vlasov–Maxwell system given sufficiently regular finite energy initial data is a longstanding open problem. The main result of Glassey and Strauss (Arch Ration Mech Anal 92:59–90, 1986) shows that a solution (f, E, B) remains C 1 as long as the momentum support of f remains bounded. Alternate proofs were later given by Bouchut et al. (Arch Ration Mech Anal 170:1–15, 2003) and Klainerman and Staffilani (Commun Pure Appl Anal 1:103–125, 2002). We show that only the boundedness of the momentum support of f after projecting to any two dimensional plane is needed for (f, E, B) to remain C 1.
KeywordsGlobal Existence Singular Term Vlasov Equation Collisionless Plasma Global Regularity
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