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

Abstract

We prove that the one-dimensional Euler-Poisson system driven by the Poisson forcing together with the usual y-law pressure, y ≥ 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. © European Mathematical Society 2008.