Global regularity of two-dimensional flocking hydrodynamics
Global regularity of two-dimensional flocking hydrodynamics
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DOI：
10.1016/j.crma.2017.05.008
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发表时间：
2017-07-01
影响因子：
0.8
通讯作者：
Tadmor, Eitan
中科院分区：
文献类型：
--
作者：
He, Siming;Tadmor, Eitan
我们研究由速度对齐驱动的基于主体的动力学产生的欧拉方程组。众所周知，此类系统的平滑解必须是聚集的，即速度场的大时间行为接近极限“聚集”速度。为了解决全局规律性问题，我们在初始构型的相空间中推导了尖锐的临界阈值，该阈值表征了全局规律性，从而表征了此类二维系统的聚集行为。具体来说，我们证明了一大类亚临界初始条件，例如初始散度“不太负”并且初始谱间隙“不太大”，全局正则性始终存在。 (C) 2017 年科学院。由 Elsevier Masson SAS 出版。版权所有。
We study the systems of Euler equations that arise from agent-based dynamics driven by velocity alignment. It is known that smooth solutions to such systems must flock, namely the large-time behavior of the velocity field approaches a limiting "flocking" velocity. To address the question of global regularity, we derive sharp critical thresholds in the phase space of initial configuration that characterizes the global regularity and hence the flocking behavior of such two-dimensional systems. Specifically, we prove for that a large class of sub-criticalinitial conditions such that the initial divergence is "not too negative" and the initial spectral gap is "not too large", global regularity persists for all time. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.