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

Abstract

We establish the local-in-time existence of weak solutions to the kinetic Cucker-Smale model with singular communication weights phi(x) = |x|-alpha with alpha is an element of (0, d). In the case alpha is an element of (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 alpha is an element of (0, d - 1).

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).