zur Startseite

Heinz Siedentop

From Excess Charge of Atoms to Blow-Up of the Patlak-Keller-Segel System

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 the total mass exceeds 8π. - This is joint work with Li Chen (Mannheim).