Qianyun Miao, Changhui Tan, and Liutang Xue
Mathematical Models and Methods in Applied Sciences, Volume 31, No 3, pp. 473-524 (2021).
Abstract
We study one-dimensional Eulerian dynamics with nonlocal alignment interactions, fea- turing 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.
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doi:10.1142/S021820252150010X |
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This work is supported by NSF grant DMS #1853001 |