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.

中文翻译：

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具有正密度和无穷熵的球对称可压缩Euler方程的真空边界问题。

在存在自由真空边界的情况下，显示了在全局实时背景仿射解周围具有正密度的球对称非等熵可压缩Euler方程的全局稳定性。通过考虑负无穷大的熵，尽管密度不消失，仍可实现真空，并且我们使用一种新颖的加权能量方法，从而熵的指数将充当变化的权重，以处理真空边界的退化。球对称在原点附近引入了一个坐标奇点，为此我们采用了一种为欧拉-泊松系统开发的方法[Y。郭等。，拱门。配给。机甲。肛门 239，431-552（2021）]我们的问题。