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On the global regularity of subcritical Euler–Poisson equations with pressure

Eitan TadmorDongming Wei — 2008

Journal of the European Mathematical Society

We prove that the one-dimensional Euler–Poisson system driven by the Poisson forcing together with the usual γ -law pressure, γ 1 , admits global solutions for a large class of initial data. Thus, the Poisson forcing regularizes the generic finite-time breakdown in the 2 × 2 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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