We prove that the one-dimensional Euler–Poisson system driven by the Poisson forcing together with the usual -law pressure, , 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.
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Eitan Tadmor, Dongming Wei, On the global regularity of subcritical Euler–Poisson equations with pressure. J. Eur. Math. Soc. 10 (2008), no. 3, pp. 757–769DOI 10.4171/JEMS/129