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

Abstract

We consider the kinetic Cucker–Smale model with super-Coulombic communication weights ϕ(r)=r−γ, γ∈(d−1,d+1/4)∖{d}. Here d∈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. γ∈(d,d+1/4), we additionally make use of the averaging lemma.