HOLDER CONTINUOUS SOLUTIONS TO THE KINETIC CUCKER-SMALE MODEL WITH SUPER-COULOMBIC SINGULAR WEIGHTS

Abstract

In this paper, we provide the local-in-time existence and uniqueness of H & ouml;lder continuous solutions to the kinetic Cucker-Smale model with super-Coulombic singular communication weights phi(alpha)(x) = |x|(-alpha) with alpha is an element of (d-1,d), d >= 2. We construct the local-in-time unique C-0,C-beta-solution with beta > 1 - (d-alpha) based on the method of characteristics. The stability of constructed solutions is obtained in the negative Sobolev space H-center dot(-(d-alpha))(R(d )x R-d).

In this paper, we provide the local-in-time existence and uniqueness of H¨older continuous solutions to the kinetic Cucker–Smale model with super-Coulombic singular communication weights ϕα(x) = |x|−α with α ∈ (d − 1, d), d ≥ 2. We construct the local-in-time unique C 0,β-solution with β > 1 − (d − α) based on the method of characteristics. The stability of constructed solutions is obtained in the negative Sobolev space H˙ −(d−α)(Rd×Rd).