ON WEAK SOLUTIONS TO THE KINETIC CUCKER-SMALE MODEL WITH SINGULAR COMMUNICATION WEIGHTS

초록

We establish the local-in-time existence of weak solutions to the kinetic Cucker–Smale model with singular communication weights φ(x) = |x| −α with α ∈ (0, d). In the case α ∈ (0, d − 1], we also provide the uniqueness of weak solutions extending the work of Carrillo et al [MMCS, ESAIM Proc. Surveys, vol. 47, EDP Sci., Les Ulis, 2014, pp. 17–35] where the existence and uniqueness of weak solutions are studied for α ∈ (0, d − 1).

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