JOURNAL OF DIFFERENTIAL EQUATIONS | 卷:257 |
Global existence of strong solution for the Cucker-Smale-Navier-Stokes system | |
Article | |
Bae, Hyeong-Ohk1  Choi, Young-Pil2  Ha, Seung-Yeal3  Kang, Moop-Jin4  | |
[1] Ajou Univ, Dept Financial Engn, Suwon 443749, South Korea | |
[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England | |
[3] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea | |
[4] Univ Texas Austin, Dept Math, Austin, TX 78712 USA | |
关键词: Cucker-Smale flocking particle; Compressible Navier-Stokes equations; Kinetic Cucker-Smale model; Strong solution; Asymptotic flocking behavior; | |
DOI : 10.1016/j.jde.2014.05.035 | |
来源: Elsevier | |
【 摘 要 】
We present a global existence theory for strong solution to the Cucker-Smale-Navier-Stokes system in a periodic domain, when initial data is sufficiently small. To model interactions between flocking particles and an incompressible viscous fluid, we couple the kinetic Cucker-Smale model and the incompressible Navier-Stokes system using a drag force mechanism that is responsible for the global flocking between particles and fluids. We also revisit the emergence of time-asymptotic flocking via new functionals measuring local variances of particles and fluid around their local averages and the distance between local averages velocities. We show that the particle and fluid velocities are asymptotically aligned to the common velocity, when the viscosity of the incompressible fluid is sufficiently large compared to the sup-norm of the particles' local mass density. (C) 2014 Elsevier Inc. All rights reserved.
【 授权许可】
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【 预 览 】
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