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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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A hydrodynamic model for the interaction of Cucker-Smale particles and incompressible fluid

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Title
A hydrodynamic model for the interaction of Cucker-Smale particles and incompressible fluid
Author
Ha, Seung-YeolKang, Moon-JinKwon, Bongsuk
Keywords
Cucker-Smale model;  flocking dissipation;  Navier-Stokes equations;  pressureless Euler equations
Issue Date
201404
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Citation
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, v., no.2, pp. -
Abstract
We present a new hydrodynamic model for the interactions between collision-free Cucker-Smale flocking particles and a viscous incompressible fluid. Our proposed model consists of two hydrodynamic models. For the Cucker-Smale flocking particles, we employ the pressureless Euler system with a non-local flocking dissipation, whereas for the fluid, we use the incompressible Navier-Stokes equations. These two hydrodynamic models are coupled through a drag force, which is the main flocking mechanism between the particles and the fluid. The flocking mechanism between particles is regulated by the Cucker-Smale model, which accelerates global flocking between the particles and the fluid. We show that this model admits the global-in-time classical solutions, and exhibits time-asymptotic flocking, provided that the initial data is appropriately small. In the course of our analysis for the proposed system, we first consider the hydrodynamic Cucker-Smale equations (the pressureless Euler system with a non-local flocking dissipation), for which the global existence and the time-asymptotic behavior of the classical solutions are also investigated.
URI
http://scholarworks.unist.ac.kr/handle/201301/4548
DOI
http://dx.doi.org/10.1142/S0218202514500225
ISSN
0218-2025
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