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Chen, Li and Siedentop, Heinz (2017): Blow-up of solutions to the Patlak-Keller-Segel equation in dimension nu >= 2. In: Applied Mathematics Letters, Vol. 74: pp. 102-107

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We prove a blow-up criterion for the solutions to the v-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 8 pi.

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