论文标题
球形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
The vacuum boundary problem for the spherically symmetric compressible Euler equations with positive density and unbounded entropy
论文作者
论文摘要
在存在自由真空边界的情况下，显示了球形对称的非分解可压缩欧拉方程的球形非分解可压缩欧拉方程的全球稳定性。尽管通过负面的熵，我们可以实现真空，但我们使用了一种新型的加权能法，熵的指数将作为变化的权重来处理真空边界的堕落。球形对称性引入了一个坐标奇异性附近，我们适应了郭，hadžić和Jang为Euler-Poisson System开发的一种方法，以解决我们的问题。
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, Hadžić and Jang to our problem.
