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arXiv · 1610.06684

Blow-up for a Three Dimensional Keller-Segel Model with Consumption of Chemoattractant

Jie Jiang·Hao Wu·Songmu Zheng
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Abstract

We investigate blow-up properties for the initial-boundary value problem of a Keller-Segel model with consumption of chemoattractant when the spatial dimension is three. Through a kinetic reformulation of the Keller-Segel model, we first derive some higher-order estimates and obtain certain blow-up criteria for the local classical solutions. These blow-up criteria generalize the results in [4,5] from the whole space $\mathbb{R}^3$ to the case of bounded smooth domain $\Omega\subset \mathbb{R}^3$. Lower global blow-up estimate on $\|n\|_{L^\infty(\Omega)}$ is also obtained based on our higher-order estimates. Moreover, we prove local non-degeneracy for blow-up points.

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Jie Jiang, Hao Wu, Songmu Zheng. 2016-10-21. Blow-up for a Three Dimensional Keller-Segel Model with Consumption of Chemoattractant. https://doi.org/10.1016/j.jde.2018.01.004

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