Blow-up of solutions to the Patlak-Keller-Segel equation in dimension nu >= 2

Chen, Li und 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

Abstract

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0893-9659
• Language: English