The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we consider a ‘spherical piston’ problem for the relativistic Euler equations, which describes the wave motion produced by a sphere expanding into an infinite surrounding medium. We use the reflected characteristics method to construct a global piecewise smooth solution with a single shock of this spherical piston problem, provided that the speed of the sphere is a small perturbation of a constant speed.

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相对论欧拉方程的三维球形活塞问题的全局解

球对称运动的研究对于爆炸波理论具有重要意义。在本文中，我们考虑了相对论欧拉方程的“球形活塞”问题，该方程描述了球体膨胀到无限的周围介质中所产生的波动。假设球体的速度是恒速的一个小扰动，我们使用反射特征法构造这个球形活塞问题的单次冲击的全局分段光滑解。