Self-similar solutions of the spherically symmetric Euler equations for general equations of state

2020/03/23 by Chen, Jianjun, Lai, Geng
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.10256

Abstract

The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we construct rigorously self-similar solutions to the Riemann problem of the spherically symmetric Euler equations for general equations of state. We used the assumption of self-similarity to reduce the spherically symmetric Euler equations to a system of nonlinear ordinary differential equations, from which we obtain detailed structures of solutions besides their existence.

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