ASYMPTOTIC FLOCKING DYNAMICS OF CUCKER-SMALE PARTICLES IMMERSED IN COMPRESSIBLE FLUIDS
ASYMPTOTIC FLOCKING DYNAMICS OF CUCKER-SMALE PARTICLES IMMERSED IN COMPRESSIBLE FLUIDS
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DOI：
10.3934/dcds.2014.34.4419
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发表时间：
2014-05
影响因子：
1.1
通讯作者：
Hyeong‐Ohk Bae;Young-Pil Choi;Seung‐Yeal Ha;Moon-Jin Kang
中科院分区：
文献类型：
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作者：
Hyeong‐Ohk Bae;Young-Pil Choi;Seung‐Yeal Ha;Moon-Jin Kang
我们提出了一个cucker -小簇粒子与粘性可压缩流体相互作用的耦合系统，并给出了该模型在空间周期域$\mathbb{T}^3$上的全局存在性理论和时间渐近行为。我们的模型由用于聚集粒子的动力学cucker - small模型和用于流体的等熵可压缩Navier-Stokes方程组成，这两个模型通过一个阻力耦合，该阻力负责粒子与流体之间的渐近对齐。对于渐近群集行为，我们明确地构造了一个Lyapunov泛函来度量与渐近群集状态的偏差。对于大粘度和小初始数据，我们表明，cucker - small颗粒和流体的速度渐近地对准共同速度。
We propose a coupled system for the interaction between Cucker-Smale flocking particles and viscous compressible fluids, and present a global existence theory and time-asymptotic behavior for the proposed model in the spatial periodic domain $\mathbb{T}^3$. 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.