The movement of a particle according to the Gurevich–Zybin dark matter model

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.