Discrete Cucker-Smale's flocking model with a weakly singular weight

TL;DR

This paper proves the existence and uniqueness of global solutions for a discrete flocking model with a weakly singular communication weight, showing the velocity component is absolutely continuous in certain weak solutions.

Contribution

It establishes the absolute continuity of velocity in weak solutions and guarantees global solution existence and uniqueness for the discrete Cucker-Smale model with a singular weight.

Findings

Velocity component is absolutely continuous in certain weak solutions.

Existence and uniqueness of global solutions are proven.

Results apply to weights with singularity parameter 0<α<1/2.

Abstract

For the discrete Cucker-Smale's flocking model with a singular communication weight $\psi(s) = s^{-\alpha}$, with $0<\alpha<1/2$ , we prove that the velocity component of certain type of weak solutions is absolutly continuous. This result enables us to obtain existence and uniqeness of global solutions.