Existence of piecewise weak solutions of a discrete Cucker–Smale's flocking model with a singular communication weight

We prove existence of global C1C1 piecewise weak solutions for the discrete Cucker–Smale's flocking model with a non-Lipschitz communication weight ψ(s)=s−αψ(s)=s−α, 0<α<10<α<1. We also discuss the possibility of finite in time alignment of the velocities of the particles.