Communications in Mathematical Sciences

Volume 10 (2012)

Number 2

On collision-avoiding initial configurations to Cucker-Smale type flocking models

Pages: 625 – 643

DOI: https://dx.doi.org/10.4310/CMS.2012.v10.n2.a10

Authors

Shin Mi Ahn (Department of Mathematical Sciences, Seoul National University, Korea)

Heesun Choi (Department of Mathematical Sciences, Seoul National University, Korea)

Seung-Yeal Ha (Department of Mathematical Sciences, Seoul National University, Korea)

Ho Lee (Max-Planck-Institute for Gravitational Physics, Albert-Einstein-Institute, Golm, Germany)

Abstract

We present a class of initial-configurations for the Cucker-Smale flocking type models leading no finite-time collisions between particles. For this class of initial-configurations, the global existence of smooth solutions to the Cucker-Smale model with singular communication weights is established. This also generalizes the earlier flocking estimates for the Cucker-Smale type models with regular communication weights.

Keywords

Cucker-Smale model, inter-particle bonding force, collision-avoidance, configuration energy

2010 Mathematics Subject Classification

74A25, 76N10, 92D25

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Published 21 December 2011