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 $ψ(s)=s^{-α}, 0<α<1.$ We also discuss the possibility of finite in time alignment of the velocities of the particles.

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