We consider the nonlinear 2 × 2 Gurevich–Zybin system as a model for the one-dimensional dynamics of dark matter. In this setting, we evaluate the movement of a particle of mass subjected to a possible jump discontinuity in the hydrodynamic speed. This problem is solved by extending the concept of usual solution to the framework of a product of distributions. A brief survey of the ideas and formulas used for multiplying distributions is included, as well as a physical interpretation of the results involving the observed speed of rotation of stars in galaxies.

中文翻译：

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根据 Gurevich-Zybin 暗物质模型的粒子运动

我们将非线性2×2 Gurevich-Zybin系统视为暗物质的一维动力学模型。在这种情况下，我们评估质量粒子在流体动力学速度中可能出现跳跃不连续性的运动。这个问题是通过将常用解的概念扩展到分布乘积的框架来解决的。包括对用于乘法分布的想法和公式的简要调查，以及对涉及观察到的星系中恒星旋转速度的结果的物理解释。