Suppression of Chemotactic Singularity via Poiseuille Flow in a Self-Consistent Patlak-Keller-Segel-Navier-Stokes System

Abstract

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.