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

Davila, Juan; Del Pino, Manuel; Dolbeault, Jean; Musso, Monica; Wei, Juncheng (2019), Infinite time blow-up in the Keller-Segel system: existence and stability. https://basepub.dauphine.fr/handle/123456789/20449

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02394787
Date
2019
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
22
Metadata
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Author(s)
Davila, Juan
Department of Mathematical Sciences, University of Bath
Del Pino, Manuel
Department of Mathematical Sciences, University of Bath
Dolbeault, Jean cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Musso, Monica
Department of Mathematical Sciences, University of Bath

Wei, Juncheng
University of British Columbia
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.
Subjects / Keywords
Patlak-Keller-Segel system; chemotaxis; critical mass; blow-up; infinite time blow-up; inner-outer gluing scheme; rate; blow-up profile