SELF-SIMILAR SOLUTIONS OF THE SPHERICALLY SYMMETRIC EULER EQUATIONS FOR GENERAL EQUATIONS OF STATE

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.