English

Global regularity for a 1D Euler-alignment system with misalignment

Analysis of PDEs 2020-04-09 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2004.03652,
  title  = {Global regularity for a 1D Euler-alignment system with misalignment},
  author = {Qianyun Miao and Changhui Tan and Liutang Xue},
  journal= {arXiv preprint arXiv:2004.03652},
  year   = {2020}
}

Comments

38 pages, 1 figure

R2 v1 2026-06-23T14:43:26.830Z