Local and Global Results on Three Dimensional Rarefaction Waves in Spherical Symmetry

TL;DR

This paper constructs and analyzes both local and global rarefaction wave solutions for the three-dimensional compressible Euler equations in spherical symmetry, advancing understanding of wave behavior in such flows.

Contribution

It establishes the existence of local and global rarefaction solutions in 3-D spherical symmetry, extending previous results to more general background states.

Findings

Existence of local rarefaction waves for general background solutions.

Global rarefaction waves exist near constant states with decay.

Results apply to the homentropic flow of perfect gases in 3-D spherical symmetry.

Abstract

We construct centered rarefaction wave solutions given background solutions to the compressible Euler equations. The flow considered in this article is the homentropic flow of perfect gas governed by compressible Euler equations and the gamma-law equation of state in 3-D spherical symmetry. We prove the existence of local in time rarefactions for general background solutions, which corresponds to one side of the solution to the Riemann problem in spherical symmetry. We also prove the existence of global in time rarefactions for background solutions that are close to constant states with reasonable decay.