Abstract
Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in the presence of free vacuum boundaries. Vacuum is achieved despite a non-vanishing density by considering a negatively unbounded entropy, and we use a novel weighted energy method, whereby the exponential of the entropy will act as a changing weight to handle the degeneracy of the vacuum boundary. Spherical symmetry introduces a coordinate singularity near the origin for which we adopt a method developed for the Euler–Poisson system [Y. Guo et al., Arch. Ration. Mech. Anal. 239, 431–552 (2021)] to our problem.
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