Strichartz estimates and moment bounds for the relativistic Vlasov-Maxwell system II. Continuation criteria in the 3D case

Abstract

We consider the $3$-dimensional relativistic Vlasov-Maxwell system with data without compact support in momentum space. We prove two continuation criteria for solutions to this system. First, we show that a regular solution can be continued if the integral of the electromagnetic field along any characteristic is assumed to be bounded. This can be viewed as a generalization of the classical result of Glassey-Strauss (1986) to data with non-compact momentum support. Second, we extend the methods in our companion paper (Part I) to show that a regular solution can be extended as long as $\|\pel_0^þ f \|_{L^q_xL^1_{\pel}}$ remains bounded for $þ>\frac{2}{q}$, $2<q\le \infty$. This improves previous results of Pallard (2005).

37 pages, submitted

References in corpus (2)

• A new continuation criterion for the relativistic Vlasov-Maxwell system
• Classical solvability of the relativistic Vlasov-Maxwell system with bounded spatial density

Cited by in corpus (5)

• On the 3D Relativistic Vlasov-Maxwell System with large Maxwell field
• Long time estimates for the Vlasov-Maxwell system in the non-relativistic limit
• Asymptotic properties of the solutions to the Vlasov-Maxwell system in the exterior of a light cone
• On propagation of higher space regularity for non-linear Vlasov equations
• Semi-classical limit of the massive Klein-Gordon-Maxwell system toward the relativistic Euler-Maxwell system via an adapted modulated energy method