Blowup of Regular Solutions for the Relativistic Euler-Poisson Equations

TL;DR

This paper investigates the conditions under which solutions to the relativistic Euler-Poisson equations blow up, providing new criteria that are valid regardless of the speed constraints, advancing understanding of singularity formation.

Contribution

It introduces new blowup conditions for the relativistic Euler-Poisson equations using a general family of testing functions, independent of speed restrictions.

Findings

Established new blowup criteria for relativistic Euler-Poisson equations.

Proved blowup conditions are valid without speed restrictions.

Enhanced understanding of singularity formation in relativistic fluid models.

Abstract

In this paper, we study the blowup phenomena for the regular solutions of the isentropic relativistic Euler-Poisson equations with a vacuum state in spherical symmetry. Using a general family of testing functions, we obtain new blowup conditions for the relativistic Euler-Poisson equations. We also show that the proposed blowup conditions are valid regardless of the speed requirement, which was one of the key constraints stated in "Y. Geng, Singularity Formation for Relativistic Euler and Euler-Poisson Equations with Repulsive Force, Commun. Pure Appl. Anal., 14 (2015), 549--564.".