The Euler--Maxwell system for electrons: global solutions in $2D$
  A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the "one-fluid" Euler--Maxwell model for electrons, in 2 spatial dimensions, and prove global stability of a constant neutral background. 
Yu Deng, Alexandru D. Ionescu, Benoit Pausader
math.AP