Global existence of spherically symmetric solutions for isothermal Euler‐Poisson system outside a ball

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