A Local Sensitivity Analysis for the Kinetic Cucker-smale Equation with Random Inputs

We present a local sensitivity analysis for the kinetic Cucker-Smale (C-S) equation with random inputs. This is a companion work to our previous local sensitivity analysis for the particle C-S model. Random imputs in the coefficients of the kinetic C-S equation can be caused by diverse sources such as the incomplete measurement and interactions with unknown environments, and will enter the problem through the communication function or initial data. For the proposed random kinetic C-S equation, we present sufficient conditions for the pathwise well-posedness and flocking estimates. For the local sensitivity analysis, we study the propagation of regularity of the kinetic density function in random space.