A collisionless plasma is modeled by the Vlasov-Maxwell system. In the presence of very large velocities, relativistic corrections are meaningful. When magnetic effects are ignored this formally becomes the relativistic Vlasov-Poisson equation. The initial value for the phase space density f0(x,v) is assumed to be sufficiently smooth, nonnegative and cylindrically symmetric. If the (two-dimensional) angular momentum is bounded away from zero on the support of f0(x,v), it is shown that a smooth solution to the Cauchy problem exists for all times.
This is joint work with Jack Schaeffer
of Carnegie Mellon University.