We study one-dimensional Eulerian dynamics with nonlocal alignment interactions, featuring strong short-range alignment, and long-range misalignment. Compared with the well-studied Euler-alignment system, the presence of the misalignment brings different behaviors of the solutions, including the possible creation of vacuum at infinite time, which destabilizes the solutions. We show that with a strongly singular short-range alignment interaction, the solution is globally regular, despite the effect of misalignment.

中文翻译：

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具有错位的一维欧拉对齐系统的全局规律性

我们研究具有非局部对齐相互作用的一维欧拉动力学，具有强短程对齐和长程错位。与经过充分研究的欧拉对齐系统相比，未对齐的存在带来了解的不同行为，包括可能在无限时间产生真空，从而使解不稳定。我们表明，尽管存在未对准的影响，但通过强烈奇异的短程对齐交互，解决方案是全局规则的。