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Kwon, Bongsuk
Partial Differential Equations and their applications
Research Interests
  • Partial differential equations, hyperbolic conservation laws, stability of nonlinear waves

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Emergent Dynamics for the Hydrodynamic Cucker--Smale System in a Moving Domain

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Title
Emergent Dynamics for the Hydrodynamic Cucker--Smale System in a Moving Domain
Author
Ha, Seung-YealKang, Moon-JinKwon, Bongsuk
Issue Date
2015-10
Publisher
SIAM PUBLICATIONS
Citation
SIAM JOURNAL ON MATHEMATICAL ANALYSIS , v.47, no.5, pp.3813 - 3831
Abstract
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.
URI
https://scholarworks.unist.ac.kr/handle/201301/17401
URL
http://epubs.siam.org/doi/abs/10.1137/140984403
DOI
10.1137/140984403
ISSN
0036-1410
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