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

초록

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).

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