Local well-posedness for the kinetic Cucker-Smale model with super-Coulombic communication weights

We consider the kinetic Cucker-Smale model with super-Coulombic communication weights phi (r) = r-gamma , gamma is an element of (d - 1, d + 1/4) \ {d}. Here d is an element of N denotes the dimension of the spatial domain. By taking into account the singular communication weight as the Fourier multiplier, we establish the local-in-time well-posedness for that kinetic equation in a weighted Sobolev space. In the case of hypersingular communication weights, i.e. gamma is an element of (d, d + 1/4), we additionally make use of the averaging lemma. (c) 2023 Elsevier Inc. All rights reserved.