标题： 球对称可压缩欧拉方程的真空边界问题，具有正密度和无界熵 显示英文标题

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

摘要： 球对称非等熵可压缩欧拉方程在全局时间背景仿射解周围具有正密度的全局稳定性在自由真空边界存在的情况下得到证明。通过考虑负无界熵，尽管密度不为零，仍实现了真空，并我们使用一种新颖的加权能量方法，其中熵的指数将作为变化的权重来处理真空边界的退化性。球对称性在原点附近引入了一个坐标奇异性，为此我们适应了Guo、Hadžić和Jang为欧拉-泊松系统开发的方法到我们的问题中。 显示英文摘要

摘要： 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 adapt a method developed for the Euler-Poisson system by Guo, Had\v{z}i\'c and Jang to our problem.