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arXiv · 2402.16536

Global well-posedness of the 3D Patlak-Keller-Segel system near a straight line

Bowei Tu
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Abstract

We consider the Cauchy problem of the three-dimensional parabolic-elliptic Patlak-Keller-Segel chemotactic model. The initial data is almost a Dirac measure supported on a straight line with mass less than $8\pi$. We prove that if the data is sufficiently close to the straight line, then global well-posedness holds. This result is parallel to the work on vortex filament solutions of the Navier-Stokes equations by Bedrossian, Germain and Harrop-Griffiths \cite{filament}.

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Bowei Tu. 2024-02-26. Global well-posedness of the 3D Patlak-Keller-Segel system near a straight line. https://arxiv.org/abs/2402.16536

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