Stable self-similar blowup for the Keller-Segel model in three dimensions

Irfan Glogić (U of Vienna)

May 21. 2024, 11:15 — 12:15

We consider the parabolic elliptic Keller-Segel model for bacterial chemotaxis. We concentrate on the three-dimensional case, for which this model arises also as a simplified version of the isothermal Euler-Poisson system modeling stellar dynamics. From the work of Brenner et al. in 1999, it is known that the 3D Keller-Segel model admits an explicit radial imploding self-similar solution. We prove the nonlinear radial asymptotic stability of this blowup profile. For this, we develop a stability analysis framework that applies to a large class of semilinear parabolic equations. In particular, we outline a robust technique to treat the underlying spectral problems. This is joint work with Birgit Schörkhuber (Innsbruck).

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Nonlinear Waves and Relativity (Thematic Programme)
Organizer(s):
Roland Donninger (U of Vienna)
David Fajman (U of Vienna)
Birgit Schörkhuber (U of Innsbruck)