Exact solutions of macroscopic self-consistent electromagnetic fields   and microscopic distribution of Vlasov-Maxwell system
  Strict mathematics reveals that the strict solution of a Vlasov-Maxwell equation set cannot be of a zero-temperature mathematical form. This universal property of Vlasov-Maxwell system can lead to a closed equation set of three macroscopic quantities: selfconsistent fields E, B and fluid velocity u, and hence their exact solutions.Strict solution of microscoipc distribution governed by self-consistent electromagnetic fields is found to be a universal extension of well-known BGK mode, which corresponds to electrostatic case. 
H. Lin
physics.plasm-ph