EXISTENCE AND STABILITY OF UNIDIRECTIONAL FLOCKS IN HYDRODYNAMIC EULER ALIGNMENT SYSTEMS
EXISTENCE AND STABILITY OF UNIDIRECTIONAL FLOCKS IN HYDRODYNAMIC EULER ALIGNMENT SYSTEMS
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DOI：
10.2140/apde.2022.15.175
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发表时间：
2022-01-01
期刊：
影响因子：
2.2
通讯作者：
Shvydkoy, Roman
中科院分区：
文献类型：
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作者：
Lear, Daniel;Shvydkoy, Roman
我们揭示了新的类的解决方案，流体动力学欧拉对齐系统管理集体行为的羊群。的解决方案描述单向平行运动的代理和全球性的良好构成的多维设置受到类似的一维情况下的阈值条件。我们发展了这些解决方案的植绒和稳定性理论，并显示出长时间收敛到一个行波与快速对齐的速度场。在Shvkirkoy和Tadmor（多尺度模型。你好19：2（2021），1115-1141）我们的解决方案可以叠加成天皇形成-指向不同方向的单向群簇。这样的形成表现出多尺度对齐现象，并类似于相互作用的大群体的现实行为。
We reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of flocks. The solutions describe unidirectional parallel motion of agents and are globally well-posed in multidimensional settings subject to a threshold condition similar to the one-dimensional case. We develop the flocking and stability theory of these solutions and show long-time convergence to a traveling wave with rapidly aligned velocity field. In the context of multiscale models introduced by Shvydkoy and Tadmor (Multiscale Model. Simul. 19:2 (2021), 1115-1141) our solutions can be superimposed into Mikado formations - clusters of unidirectional flocks pointing in various directions. Such formations exhibit multiscale alignment phenomena and resemble realistic behavior of interacting large flocks.