Communications in Mathematical Sciences
Volume 19 (2021)
Self-similar solutions of the spherically symmetric Euler equations for general equations of state
Pages: 1991 – 2018
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 use 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.
compressible Euler equations, van der Waals gas, spherical symmetry, self-similar solution
2010 Mathematics Subject Classification
35L60, 35L65, 35L67
The first-named author was partially supported by the Natural Science Foundation of Zhejiang Province (LQ19A010003).
The second-named author was partially supported by the National Natural Science Foundation of China (NSFC 12071278).
Received 26 January 2019
Accepted 20 April 2021
Published 7 September 2021