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 $C^1$ 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 $C^1$.

21 pages, to appear in Commun. Math. Phys

References in corpus (1)

• Classical solvability of the relativistic Vlasov-Maxwell system with bounded spatial density

Cited by in corpus (3)

• Strichartz estimates and moment bounds for the relativistic Vlasov-Maxwell system I. The $2$-D and $2\frac{1}{2}$-D cases
• Strichartz estimates and moment bounds for the relativistic Vlasov-Maxwell system II. Continuation criteria in the 3D case
• On the 3D Relativistic Vlasov-Maxwell System with large Maxwell field