TY - JOUR
T1 - Suppression of Chemotactic Singularity via Poiseuille Flow in a Self-Consistent Patlak-Keller-Segel-Navier-Stokes System
AU - Li , Hao
AU - Peng , Yingping
AU - Xiang , Zhaoyin
JO - Communications in Mathematical Analysis and Applications
VL - 2
SP - 234
EP - 284
PY - 2025
DA - 2025/06
SN - 4
DO - http://doi.org/10.4208/cmaa.2025-0004
UR - https://global-sci.org/intro/article_detail/cmaa/24123.html
KW - Suppression of chemotactic singularity, Poiseuille flow, self-consistent, fully
parabolic Patlak-Keller-Segel-Navier-Stokes system.
AB - <p style="text-align: justify;">In this paper, we investigate a fully parabolic Patlak-Keller-Segel-Navier-Stokes system with a self-consistent mechanism near the Poiseuille flow $A(y^2,0)$ in $\mathbb{T}×\mathbb{R},$ which is more natural than the Couette flow from a biomathematical perspective. We demonstrate that the solution to this system maintains
global regularity, provided the amplitude $A$ is suitably large and the non-zero
modes of the initial chemical density and vorticity are suitably small. To avoid
the complex study of the spectral properties of the linear operator and its resolvent, we prove our result using a straightforward weighted energy method
combined with a bootstrap argument.</p>