Stability of infinite time blow up for the Patlak Keller Segel system
Abstract
We consider the parabolic-elliptic Patlak-Keller-Segel (PKS) model of chemotactic aggregation in two space dimensions which describes the aggregation of bacteria under chemo-taxis. When the mass is equal to 8π and the second moment is finite (the doubly critical case), we give a precise description of the dynamic as time goes to infinity and extract the limiting profile and speed. The proof shows that this dynamic is stable under perturbations.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.