We study the Cucker–Smale (CS) flocking systems involving both singularity and noise. We first show the local strong well-posedness for the stochastic singular CS systems before the first collision time, which is a well-defined stopping time. Then, for communication with higher order singularity at origin (corresponding to α ≥ 1 in the case of ψ(r) = r−α), we establish the global well-posedness by showing the collision-avoidance in finite time, provided that there is no initial collisions and the initial velocities have finite moment of any positive order. Finally, we study the large time behavior of the solution when ψ is of zero lower bound, and provide the emergence of conditional flocking or unconditional flocking in the mean sense, for constant and square integrable intensity, respectively.

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关于随机奇异 Cucker-Smale 模型：适定性、防撞和植绒

我们研究了涉及奇点和噪声的 Cucker-Smale (CS) 植绒系统。我们首先展示了随机奇异 CS 系统在第一次碰撞时间之前的局部强适定性，这是一个明确定义的停止时间。然后，对于在原点具有高阶奇点的通信（对应于α ≥ 1如果是ψ(r) = r-α），我们通过显示有限时间内的碰撞避免来建立全局适定性，前提是没有初始碰撞并且初始速度具有任何正阶的有限矩。最后，我们研究了解的大时间行为，当ψ是零下限，并在平均意义上提供条件植绒或无条件植绒的出现，分别用于恒定和平方可积强度。