Blowup Behavior of Radial Solutions to Jäger-Luckhaus System in High Dimensional Domains

Abstract

In this paper, we will consider the blowup and the time-global existence of radial solutions to a simplified system of the so called Keller-Segel model in a domain of three or more dimensional Euclidean space. In the two dimensional case, the blowup solutions have a delta function singularity at each blowup point (see [13]). However, in the three dimensional case, Herrero, Medina and Velázquez [7] show that there exist self-similar blowup solutions and that the solutions have a singularity which is different from a delta function singularity. In this paper, we will consider the blowup criterion and the blowup self-similar solutions in the three or more dimensional cases.