On collision-avoiding initial configurations to Cucker-Smale type flocking models

We present a class of initial-configurations for the Cucker-Smale flocking type models leading no finite-time collisions between particles. For this class of initial-configurations, the global existence of smooth solutions to the Cucker-Smale model with singular communication weights is established. This also generalizes the earlier flocking estimates for the Cucker-Smale type models with regular communication weights.