EMERGENT DYNAMICS FOR THE HYDRODYNAMIC CUCKER-SMALE SYSTEM IN A MOVING DOMAIN

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We study the emergent dynamics for the hydrodynamic Cucker-Smale system arising in the modeling of flocking dynamics in interacting many-body systems. Specifically, the initial value problem with a moving domain is considered to investigate the global existence and time-asymptotic behavior of classical solutions, provided that the initial mass density has bounded support and the initial data are in an appropriate Sobolev space. In order to show the emergent behavior of flocking, we make use of an appropriate Lyapunov functional that measures the total fluctuation in the velocity relative to the mean velocity. In our analysis, we present the local well-posedness of the smooth solutions via Lagrangian coordinates, and we extend to the global-in-time solutions by establishing the uniform flocking estimates.
Publisher
SIAM PUBLICATIONS
Issue Date
2015-10
Language
English
Article Type
Article
Citation

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v.47, no.5, pp.3813 - 3831

ISSN
0036-1410
DOI
10.1137/140984403
URI
http://hdl.handle.net/10203/278729
Appears in Collection
MA-Journal Papers(저널논문)
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