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Global stability of the spherically symmetric nonisentropic compressibleEuler equations with positive density around global-in-time background affinesolutions is shown in the presence of free vacuum boundaries. Vacuum isachieved despite a non-vanishing density by considering a negatively unboundedentropy and we use a novel weighted energy method whereby the exponential ofthe entropy will act as a changing weight to handle the degeneracy of thevacuum boundary. Spherical symmetry introduces a coordinate singularity nearthe origin for which we adapt a method developed for the Euler-Poisson systemby Guo, Had\v{z}i\'c and Jang to our problem.

The vacuum boundary problem for the spherically symmetric compressible Euler equations with positive density and unbounded entropy