A new continuation criterion for the relativistic Vlasov-Maxwell system
Abstract
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-Strauss (1986) shows that a solution (f, E, B) remains C1 as long as the momentum support of f remains bounded. Alternate proofs were later given by Bouchut-Golse-Pallard (2003) and Klainerman-Staffilani (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 C1.
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