In this paper, we present quantitative local sensitivity estimates for the kinetic chemotaxis Cucker-Smale(CCS) equation with random inputs. In the absence of random inputs, the kinetic CCS model exhibits velocity alignment under suitable structural assumptions on the turning kernel and reaction term despite of the random effect due to a turning operator. We provide a global existence of a regular solution with slow velocity alignment for the random kinetic CCS model within the proposed framework. Moreover, we investigate the propagation of regularity and stability of infinitesimal variations in random space.

中文翻译：

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具有趋化运动的随机动力学Cucker-Smale模型的定量局部敏感性估计

在本文中，我们提出了带有随机输入的动力学趋化性Cucker-Smale（CCS）方程的定量局部灵敏度估计。在没有随机输入的情况下，尽管由于旋转算子而产生随机效应，但动力学CCS模型在适当的结构假设下对车削核和反作用项仍表现出速度对准。我们为提出的框架内的随机动力学CCS模型提供了具有慢速速度校正的正则解的整体存在性。此外，我们研究了随机空间中无穷小变化的规律性和稳定性的传播。