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arXiv · 2405.02562

Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part I: Alternating Flows

Siming He
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Abstract

We consider the three-dimensional parabolic-parabolic Patlak-Keller-Segel equations (PKS) subject to ambient flows. Without the ambient fluid flow, the equation is super-critical in three-dimension and has finite-time blow-up solutions with arbitrarily small $L^1$-mass. In this study, we show that a family of time-dependent alternating shear flows, inspired by the clever ideas of Tarek Elgindi, can suppress the chemotactic blow-up in these systems.

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Siming He. 2024-05-04. Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part I: Alternating Flows. https://arxiv.org/abs/2405.02562

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