A local sensitivity analysis for the hydrodynamic Cucker-Smale model with random inputs

We present a local sensitivity analysis for the hydrodynamic Cucker-Smale (HCS) model with random inputs. In the absence of random inputs, the HCS model was derived as a macroscopic model for the emergent dynamics of the CS flocking ensemble from the kinetic CS model via the moment method and mono-kinetic ansatz for a closure condition. In this paper, we incorporate the uncertain effects together with the HCS model to result in the random HCS model. For definiteness, we consider the uncertainties in initial data and communication weight function. For this random HCS model, we perform local sensitivity estimates such as the propagation of pathwise well-posedness, pathwise L²-stability and flocking estimates of solution process.