Sharp conditions to avoid collisions in singular Cucker-Smale interactions

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Title: Sharp conditions to avoid collisions in singular Cucker-Smale interactions
Authors: Carrillo, JA
Choi, Y-P
Mucha, PB
Peszele, J
Item Type: Journal Article
Abstract: We consider the Cucker–Smale flocking model with a singular communication weight with . We provide a critical value of the exponent in the communication weight leading to global regularity of solutions or finite-time collision between particles. For , we show that there is no collision between particles in finite time if they are placed in different positions initially. For we investigate a version of the Cucker–Smale model with expanded singularity i.e. with weight , . For such model we provide a uniform with respect to the number of particles estimate that controls the -distance between particles. In case of it reduces to the estimate of collision avoidance.
Issue Date: 19-Mar-2017
Date of Acceptance: 23-Feb-2017
URI: http://hdl.handle.net/10044/1/52840
DOI: https://dx.doi.org/10.1016/j.nonrwa.2017.02.017
ISSN: 1468-1218
Publisher: Elsevier
Start Page: 317
End Page: 328
Journal / Book Title: Nonlinear Analysis: Real World Applications
Volume: 37
Copyright Statement: © 2017 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM120001
EP/P031587/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Cucker-Smale system
Flocking models
Global in time existence
Singular communication weight
Non-collisioness gases
SELF-DRIVEN PARTICLES
ORIENTATION INTERACTION
ASYMPTOTIC FLOCKING
DYNAMICS
MODEL
LIMIT
EMERGENCE
CONSENSUS
0102 Applied Mathematics
Applied Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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