On the global regularity of sub-critical Euler-Poisson equations with pressure

TL;DR

This paper proves that the one-dimensional Euler-Poisson system with gamma-law pressure admits global solutions for a broad class of initial data, showing Poisson forcing's regularizing effect on finite-time breakdown.

Contribution

It establishes conditions under which the Euler-Poisson equations with pressure have global solutions, highlighting the regularizing role of Poisson forcing.

Findings

Poisson forcing prevents finite-time breakdown in the Euler-Poisson system.

Global regularity depends on initial Riemann invariants and density crossing a critical threshold.

The results apply to a large class of initial data with gamma ≥ 1.

Abstract

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 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.