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

摘要

In (Arch. Rat. Mech. Anal. 1986; 92:59-90), Glassey and Strauss showed that if the growth in the momentum of the particles is controlled, the relativistic Vlasov-Maxwell system has classical solution globally in time. Later they proved that such control is achieved if the kinetic energy density of the particles remains bounded for all time (Math. Meth. Appl. Sci. 1987; 9:46-52). Here, we show that the latter assumption can be weakened to the boundedness of the spatial density.