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

We prove existence of global $C^1$ piecewise weak solutions for the discrete Cucker-Smale’s flocking model with the communication weight $\psi (s)=s^{-\alpha },0<\alpha <1.$ We also discuss the possibility of finite in time alignment of the velocities of the particles.