TY - JOUR
T1 - Asymptotic flocking dynamics of Cucker-Smale particles immersed in compressible fluids
AU - Bae, Hyeong Ohk
AU - Choi, Young Pil
AU - Ha, Seung Yeal
AU - Kang, Moon Jin
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/11
Y1 - 2014/11
N2 - We propose a coupled system for the interaction between Cucker-Smale ocking particles and viscous compressible fluids, and present a global existence theory and time-asymptotic behavior for the proposed model in the spatial periodic domain T3. Our model consists of the kinetic Cucker-Smale model for flocking particles and the isentropic compressible Navier-Stokes equations for fluids, and these two models are coupled through a drag force, which is responsible for the asymptotic alignment between particles and fluid. For the asymptotic flocking behavior, we explicitly construct a Lyapunov functional measuring the deviation from the asymptotic flocking states. For a large viscosity and small initial data, we show that the velocities of Cucker-Smale particles and fluids are asymptotically aligned to the common velocity.
AB - We propose a coupled system for the interaction between Cucker-Smale ocking particles and viscous compressible fluids, and present a global existence theory and time-asymptotic behavior for the proposed model in the spatial periodic domain T3. Our model consists of the kinetic Cucker-Smale model for flocking particles and the isentropic compressible Navier-Stokes equations for fluids, and these two models are coupled through a drag force, which is responsible for the asymptotic alignment between particles and fluid. For the asymptotic flocking behavior, we explicitly construct a Lyapunov functional measuring the deviation from the asymptotic flocking states. For a large viscosity and small initial data, we show that the velocities of Cucker-Smale particles and fluids are asymptotically aligned to the common velocity.
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U2 - 10.3934/dcds.2014.34.4419
DO - 10.3934/dcds.2014.34.4419
M3 - Article
AN - SCOPUS:84901804998
VL - 34
SP - 4419
EP - 4458
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
SN - 1078-0947
IS - 11
ER -