Infinite time blow-up in the Keller-Segel system: existence and stability

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Date
2019
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
12-2019
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-02394787
Dewey
Analyse
Sujet
Patlak-Keller-Segel system; chemotaxis; critical mass; blow-up; infinite time blow-up; inner-outer gluing scheme; rate; blow-up profile
URI
https://basepub.dauphine.fr/handle/123456789/20449
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Author
Davila, Juan
84406 Department of Mathematical Sciences, University of Bath
Del Pino, Manuel
84406 Department of Mathematical Sciences, University of Bath
Dolbeault, Jean
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Musso, Monica
84406 Department of Mathematical Sciences, University of Bath
109842 Departamento de Matematicas PUC
Wei, Juncheng
251768 University of British Columbia
Type
Document de travail / Working paper
Item number of pages
22
Abstract (EN)
The simplest version of the parabolic-elliptic Patlak-Keller-Segel system in the two-dimensional Euclidean space has an 8π critical mass which corresponds to the exact threshold between finite-time blow-up and self-similar diffusion towards zero. Among functions with mass 8π, we find a neighborhood of a radial function such that any solution with initial condition in this neighborhood is globally defined and blows-up in infinite time with an explicit scaling involving the square root of the logarithm of the time.