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arxiv: 1403.4975 · v1 · pith:Y5EVEXWEnew · submitted 2014-03-19 · 🧮 math.AP

Stable blow-up dynamic for the parabolic-parabolic Patlak-Keller-Segel model

Remi Schweyer This is my paper
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keywords blow-upcaseparabolic-parabolicpatlak-keller-segelstablearticleconsiderdynamic
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We consider the parabolic-parabolic two-dimensional Patlak-Keller-Segel problem. We prove the existence of stable blow-up dynamics in finite time in the radial case. We extend in this article the result of [36] for the parabolic-elliptic case.

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  1. Refined temporal asymptotics near blow-up points in the planar Keller-Segel system

    math.AP 2026-04 unverdicted novelty 5.0

    Near any blow-up point in the planar Keller-Segel system, the localized L log L norm of u satisfies limsup (1/ln(T/(T-t))) * integral >= delta_0 > 0 as t approaches the blow-up time T.