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Nonlinear Analysis

Singularity formation for the Keller-Segel system in the plane

Manuel del Pino, University of Bath

Location:  zoom
Date & time: Wednesday, 24 March 2021 at 9:30AM - 10:30AM

Abstract: The classical model for chemotaxis is the planar Keller-Segel system \[ u_t = Delta u -
ablacdot ( u
abla v ), quad v(cdot, t) = frac 1{2pi} log 1{|cdot |} * u(cdot ,t) . \]in \(R^2times (0,infty)\). 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 \(8pi\), 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. 

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