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. |