TY - JOUR
T1 - Global regularity for a 1D Euler-alignment system with misalignment
AU - Miao, Qianyun
AU - Tan, Changhui
AU - Xue, Liutang
N1 - Publisher Copyright:
© 2021 World Scientific Publishing Company.
PY - 2021/3
Y1 - 2021/3
N2 - 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.
AB - 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.
KW - Euler-alignment system
KW - global regularity
KW - misalignment
KW - modulus of continuity
UR - https://www.scopus.com/pages/publications/85101461560
U2 - 10.1142/S021820252150010X
DO - 10.1142/S021820252150010X
M3 - Article
AN - SCOPUS:85101461560
SN - 0218-2025
VL - 31
SP - 473
EP - 524
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 3
ER -