DISCRETE CUCKER-SMALE FLOCKING MODEL WITH A WEAKLY SINGULAR WEIGHT

作者：Peszek Jan^*

来源：SIAM Journal on Mathematical Analysis, 2015, 47(5): 3671-3686.

DOI：10.1137/15M1009299

• singular kernel
• singular potential
• alignment
• swarming
• flocking
• aggregation

The Cucker-Smale flocking model is one of the many aggregation and flocking models describing a collective, self-driven motion of self-propelled particles with some predefined tendency (e.g., to form a flock, to move in a specific direction). We are interested in the discrete Cucker-Smale flocking model with a singular kernel psi(s) = s(-alpha) with 0 < alpha. The Cucker-Smale model with a singular kernel possesses particularly interesting and difficult-to-analyze dynamics. Even the most basic question of well-posedness for the particle system remains open. In this paper we prove that in case of a < 1 2 the velocity component of a certain type of weak solutions is absolutely continuous. This result enables us to obtain existence and uniqueness of global solutions.

• 出版日期2015