Programa de Pós-Graduação em Matemática

Singularity formation for the Keller-Segel system in the plane

Prof. Manuel Del Pino

Date: 18th February 9:00 am - 9:45 am (UTC -3) Link: PPGM/UFSCar Youtube channel

Abstract: The classical model for chemotaxis is the planar Keller-Segel system

ut = ∆u−∇·(u∇v), v(·,t) = 1/2πlog1|·|∗u(·,t).

in R2×(0, ∞). Blow-up of finite mass solutions is expected to take place by aggregation, which is a concentration of bubbling type, common to many geometric flows. We build with precise profiles solutions in the critical- mass case 8π, in which blow-up in infinite time takes place. We establish stability of the phenomenon detected under arbitrary mass-preserving small perturbations and present new constructions in the finite time blow-up scenario.