Hydrodynamic limits for kinetic flocking models of Cucker-Smale type
File(s)
Published version
Author(s)
Aceves Sanchez, Pedro
Bostan, Mihai
Carrillo de la Plata, Jose Antonio
Degond, Pierre
Type
Journal Article
Abstract
We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The self-propelling and friction forces together with the alignment and the noise are interpreted as a collision/interaction mechanism acting with equal strength. We show that the set of generalized collision invariants, introduced in [39], is equivalent in our setting to the more classical notion of collision invariants, i.e., the kernel of a suitably linearized collision operator. After identifying these collision invariants, we derive the fluid model, by appealing to the balances for the particle concentration and orientation. We investigate the main properties of the macroscopic model for a general potential with radial symmetry.
Date Issued
2019-08-28
Date Acceptance
2019-06-05
Citation
Mathematical Biosciences and Engineering, 2019, 16 (6), pp.7883-7910
ISSN
1547-1063
Publisher
American Institute of Mathematical Sciences
Start Page
7883
End Page
7910
Journal / Book Title
Mathematical Biosciences and Engineering
Volume
16
Issue
6
Copyright Statement
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
License URL
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM130048
EP/M006883/1
EP/P013651/1
EP/P031587/1
Subjects
0102 Applied Mathematics
0903 Biomedical Engineering
0904 Chemical Engineering
Bioinformatics
Publication Status
Published
Date Publish Online
2019-08-28