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

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