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arXiv · 1701.04631

Blow-Up of Solutions to the Patlak-Keller-Segel Equation in Dimension $ν\geq2$

Li Chen·Heinz Siedentop
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Abstract

We prove a blow-up criterion for the solutions to the $ν$-dimensional Patlak-Keller-Segel equation in the whole space. The condition is new in dimension three and higher. In dimension two it is exactly Dolbeault's and Perthame's blow-up condition, i.e., blow-up occurs if total mass exceeds $8π$ .

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Li Chen, Heinz Siedentop. 2017-03-01. Blow-Up of Solutions to the Patlak-Keller-Segel Equation in Dimension $ν\geq2$. https://arxiv.org/abs/1701.04631

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