论文标题
流体动力欧拉对准系统中的单向羊群II：奇异模型
Unidirectional flocks in hydrodynamic Euler Alignment system II: Singular models
论文作者
论文摘要
在本说明中，我们继续研究具有强烈奇异的通信内核的流体动力欧拉对准系统$ ϕ（x）：= | x |^{ - （n+α）} $ for $α\ in（0,2）$。解决方案描述了管理羊群多维集体行为的代理的单向平行运动。在这里，我们考虑$ 1 <α<2 $的范围，并建立平滑解决方案的全球规律性，以及对它们长时间动态的完整描述。具体而言，我们发展了这些溶液的植入理论，并显示了与速度快速一致的速度场的长期收敛。
In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels $ϕ(x):=|x|^{-(n+α)}$ for $α\in(0,2)$. The solutions describe unidirectional parallel motion of agents governing multi-dimensional collective behavior of flocks. Here, we consider the range $1<α<2$ and establish the global regularity of smooth solutions, together with a full description of their long time dynamics. Specifically, we develop the flocking theory of these solutions and show long time convergence to traveling wave with rapidly aligned velocity field.
