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.
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