Sharp conditions to avoid collisions in singular Cucker–Smale interactions

• Published in: Nonlinear analysis: real world applications Vol. 37; pp. 317 - 328
• Main Authors: Carrillo, José A., Choi, Young-Pil, Mucha, Piotr B., Peszek, Jan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.10.2017; Elsevier BV
• Subjects: Collision avoidance; Cucker–Smale system; Flocking models; Global in time existence; Non-collisioness gases; Singular communication weight; Weight; Non-collisioness gases; Global in time existence; Cucker–Smale system; Flocking models; Singular communication weight

We consider the Cucker–Smale flocking model with a singular communication weight ψ(s)=s−α with α>0. We provide a critical value of the exponent α in the communication weight leading to global regularity of solutions or finite-time collision between particles. For α≥1, we show that there is no col...