The vacuum boundary problem for the spherically symmetric compressible Euler equations with positive density and unbounded entropy
arXiv:2010.00205 · doi:10.1063/5.0037656
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 adapt a method developed for the Euler-Poisson system by Guo, Hadžić and Jang to our problem.