A sharp local blow-up condition for Euler-Poisson equations with attractive forcing

TL;DR

This paper establishes a refined local blow-up criterion for the Euler-Poisson equations with attractive forcing, demonstrating conditions under which solutions break down in finite time across any spatial dimension.

Contribution

It improves previous results by providing a sharper one-sided threshold condition for finite-time blow-up in Euler-Poisson equations.

Findings

Finite-time breakdown under new threshold condition

Applicable to arbitrary spatial dimensions

Enhances understanding of blow-up mechanisms

Abstract

We improve the recent result of Chae & Tadmor in [Comm. Math. Sci. 6(3) (2008) 785-789], proving a one-sided threshold condition which leads to finite-time breakdown of the Euler-Poisson equations in arbitrary dimension n.