Abstract
The Cauchy problem for the relativistic Vlasov-Maxwell system in three space dimensions is considered. It is assumed that the initial data satisfy compatibility constraints and have compact spatial support. The initial particle distribution is assumed to decay rapidly for large momenta, but needn't have compact support. Then it is shown that if the initial data are sufficiently small in a certain norm then the system possesses a classical solution on all of space time. This generalizes the earlier work of Glassey and Strauss [11] which required the initial particle distribution to have compact support.
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