The study of radially symmetric motion is important for the theory of explosion waves. We construct rigorously self-similar entropy solutions to Riemann initial-boundary value problems for the radially symmetric relativistic Euler equations. We use the assumption of self-similarity to reduce the relativistic Euler equations to a system of nonlinear ordinary differential equations, from which we obtain detailed structures of solutions besides their existence. For the ultra-relativistic Euler equations, we also obtain the uniqueness of the self-similar entropy solution to the Riemann initial-boundary value problems.

中文翻译：

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径向对称相对论欧拉方程的自相似解

径向对称运动的研究对于爆炸波理论具有重要意义。我们为径向对称相对论欧拉方程构造了黎曼初边值问题的严格自相似熵解。我们利用自相似性假设将相对论欧拉方程简化为非线性常微分方程组，从中我们可以得到解的详细结构。对于超相对论的欧拉方程，我们还得到了黎曼初边值问题的自相似熵解的唯一性。