We identify and analyze the phenomena of concentration and cavitation by studying the vanishing pressure limit of solutions to a simplified isentropic relativistic Euler equations. Firstly, both the explicit expressions and geometric properties of the rarefaction wave curve and shock wave curve based on any left state are given with the help of Lorentz invariance, and the Riemann problem for this system is considered. Then, we rigorously prove that, as pressure vanishes, any two-shock Riemann solution tends to a delta-shock solution of the pressureless relativistic Euler equations, and the intermediate density between the two shocks tends to a weighted \(\delta \)-measure, which forms the delta shock wave. This describes the phenomenon of mass concentration. On the other hand, any two-rarefaction Riemann solution tends to a two-contact-discontinuity solution of the pressureless relativistic Euler equations and the nonvacuum intermediate state in between tends to a vacuum state, which reveals the phenomenon of cavitation. Both concentration and cavitation are fundamental and physical in fluid dynamics.

通过研究简化的等熵相对论欧拉方程的解的消失极限，我们识别并分析了集中和空化现象。首先，借助洛伦兹不变性，给出了基于任意左态的稀疏波曲线和冲击波曲线的显式表达式和几何性质，并考虑了该系统的黎曼问题。然后，我们严格证明，随着压力的消失，任何两震的Riemann解都趋向于无压相对论Euler方程的delta-shock解，两次冲击之间的中间密度趋于于加权\（\ delta \）-测量，形成三角波冲击波。这描述了质量集中现象。另一方面，任何两反射Riemann解都趋向于无压相对论欧拉方程的两接触间断解，并且两者之间的非真空中间态趋向于真空态，这表明了气蚀现象。集中和空化都是流体动力学的基础和物理基础。