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Local well-posedness of the generalized Cucker-Smale model

Abstract:

In this paper, we study the local well-posedness of two types of generalized Cucker-Smale (in short C-S) flocking models. We consider two different communication weights, singular and regular ones, with nonlinear coupling velocities $v|v|^{\beta-2}$ for $\beta > \frac{3-d}{2}$. For the singular communication weight, we choose $\psi^1(x) = 1/|x|^{\alpha}$ with $\alpha \in (0,d-1)$ and $\beta \geq 2$ in dimension $d > 1$. For the regular case, we select $\psi^2(x) \geq 0$ belonging to $(L...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1051/proc/201447002

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
EDP Open
Journal:
ESAIM: Proceedings and Surveys More from this journal
Volume:
47
Pages:
17 - 35
Publication date:
2014-12-18
Acceptance date:
2014-01-01
DOI:
EISSN:
2267-3059
Language:
English
Keywords:
Pubs id:
1098416
Local pid:
pubs:1098416
Deposit date:
2020-08-11

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