Robert Glassey
THE VLASOV-MAXWELL SYSTEM
 
Abstract
 The Vlasov-Maxwell equations are the equations of motion for a collisionless plasma: a high temperature,
low density ionized gas in which electromagnetic forces dominate collisional effects.  In this lecture  we  will
probe the major open question: does the initial-value problem have a smooth global solution for smooth data
of unrestricted size?  That is, are there shocks in collisionless plasmas? Partial answers and known results will
be surveyed, including weak solutions, solutions with small data, the resolution of the large-data problem in
two space dimensions and classical vs. relativistic formulations.