On the global regularity of sub-critical Euler-Poisson equations with   pressure
  We prove that the one-dimensional Euler-Poisson system driven by the Poisson forcing together with the usual &gamma;-law pressure, &gamma; &geq; 1, admits global solutions for a large class of initial data. Thus, the Poisson forcing regularizes the generic finite-time breakdown in the 2x2 p-system. Global regularity is shown to depend on whether or not the initial configuration of the Riemann invariants and density crosses an intrinsic critical threshold. 
Eitan Tadmor and Dongming Wei