Stability of a class of supercritical volume-filling chemotaxis-fluid model near Couette flow

Abstract

Consider a class of chemotaxis-fluid model incorporating a volume-filling effect in the sense of Painter and Hillen (Can. Appl. Math. Q. 2002; 10(4): 501-543), which is a supercritical parabolic-elliptic Keller-Segel system. As shown by Winkler et al., for any given mass, there exists a corresponding solution of the same mass that blows up in either finite or infinite time. In this paper, we investigate the stability properties of the two dimensional Patlak-Keller-Segel-type chemotaxis-fluid model near the Couette flow $(Ay,0)$ in $\mathbb{T}\times \mathbb{R},$ and show that the solutions are global in time as long as the initial cell mass $M<\frac{2\pi }{\sqrt{3}}$ and the shear flow is sufficiently strong ($A$ is large enough).

arXiv admin note: text overlap with arXiv:2405.10337