Communications in Mathematical Sciences

Volume 19 (2021)

Number 7

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

Pages: 1991 – 2018

DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n7.a9

Authors

Jianjun Chen (Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, China)

Geng Lai (Department of Mathematics, Shanghai University, Shanghai, China)

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 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.

Keywords

compressible Euler equations, van der Waals gas, spherical symmetry, self-similar solution

2010 Mathematics Subject Classification

35L60, 35L65, 35L67

Full Text (PDF format)

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