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### On the Conditional Global Regularity of the 1D Euler-Poisson Equations with Pressure

Dongming Wei

Center for Scientific Computation and Mathematical Modeling at University of Maryland, College Park

Abstract: 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 $2 \times 2$ p-system. Global regularity is shown to depend on whether the  initial configuration of the Riemann invariants and density crosses an intrinsic critical threshold.

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