The Euler--Poisson system in 2D: global stability of the constant   equilibrium solution
  We consider the (repulsive) Euler-Poisson system for the electrons in two dimensions and prove that small smooth perturbations of a constant background exist for all time and remain smooth (never develop shocks). This extends to 2D the work of Guo. 
Alexandru D. Ionescu and Benoit Pausader
math.AP