Singularity formation in a collisionless plasma could occur only at high velocities (Q1077627)

The global existence problem is studied for regular solutions of the relativistic Vlasov-Maxwell equations. If it is assumed that the plasma density vanishes a priori for velocities near the speed of light, then regular solutions with arbitrary initial data exist in all of space and time. This assumption is either postulated for a solution or is arranged for all solutions through a modification of the equations themselves. The method involves replacing the usual partial derivatives in \(x,t\) by three tangential derivatives (from Maxwell's equations) and the linear transport operator. Via integration by parts it is then possible to exploit the fact that the charge and current densities are themselves integrals over velocities.