Global existence of spherically symmetry solutions for isothermal Euler-Poisson system outside a ball

TL;DR

This paper proves the global existence of spherically symmetric solutions for the isothermal Euler-Poisson system with self-gravity outside a ball, using advanced numerical schemes and compactness theory.

Contribution

It establishes the existence of global entropy solutions for the system outside a ball, which was previously unresolved.

Findings

Existence of global entropy solutions proven.

Application of fractional Lax-Friedrichs scheme and compensated compactness.

Solutions model compact stars like strange quark stars.

Abstract

In this paper, we consider an isothermal Euler-Poisson system with self-gravitational force, modeling a compact star such as strange quark star. We prove that there exists a global entropy solution with spherically symmetry outside a ball, through the fractional Lax-Friedrichs scheme and the theory of compensated compactness.