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Global regularity for a 1D Euler-alignment system with misalignment
Mathematical Models and Methods in Applied Sciences ( IF 3.6 ) Pub Date : 2021-02-16 , DOI: 10.1142/s021820252150010x
Qianyun Miao 1 , Changhui Tan 2 , Liutang Xue 3
Affiliation  

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:

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。
更新日期:2021-02-16
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