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arXiv · 2410.02214

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

Lili Wang·Wendong Wang·Yi Zhang
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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).

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Lili Wang, Wendong Wang, Yi Zhang. 2024-10-03. Stability of a class of supercritical volume-filling chemotaxis-fluid model near Couette flow. https://arxiv.org/abs/2410.02214

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