Unidirectional flocks in hydrodynamic Euler alignment system II: singular models

In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels $\phi(x):=|x|^{-(n+\alpha)}$ for $\alpha\in(0,2)$. The describe parallel motion agents governing multi-dimensional collective behavior flocks. Here, consider the range $1<\alpha<2$ and establish global regularity smooth solutions, together a full description their long time dynamics. Specifically, develop flocking theory these show convergence traveling wave rapidly aligned velocity field.