We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case, the equilibria depend on the density and the orientation of the mean velocity, whereas the mean speed is not anymore a free parameter and a phase transition occurs in the homogeneous kinetic equation. We analyze the profile of equilibria for general potentials identifying a family of potentials leading to phase transitions. Finally, we derive the fluid equations when the interaction frequency becomes very large.

中文翻译：

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群体运动方程的相变流体模型

我们专注于通过自推进力和摩擦力、对齐和噪音与个体相互作用的动力学模型。我们假设每个人的速度都放松到平均速度。在我们目前的情况下，平衡取决于平均速度的密度和方向，而平均速度不再是自由参数，相变发生在均匀动力学方程中。我们分析了一般势的平衡概况，确定了一系列导致相变的势。最后，我们推导出相互作用频率变得非常大时的流体方程。