Strong solutions to the Keller-Segel system with the weak L n2 initial data and its application to the blow-up rate

Hideo Kozono, Yoshie Sugiyama

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

We shall show an exact time interval for the existence of local strong solutions to the Keller-Segel system with the initial data u0 in L n2w (Rn), the weak L n2 -space on Rn. If ||u0||L n2 w (Rn) is sufficiently small, then our solution exists globally in time. Our motivation to construct solutions in L n2w (Rn) stems from obtaining a self-similar solution which does not belong to any usual Lp(Rn). Furthermore, the characterization of local existence of solutions gives us an explicit blow-up rate of ||u(t)||Lp(Rn) for n 2 < p≤∞as t → Tmax, where Tmax denotes the maximal existence time.

Original languageEnglish
Pages (from-to)732-751
Number of pages20
JournalMathematische Nachrichten
Volume283
Issue number5
DOIs
Publication statusPublished - 2010 May 1
Externally publishedYes

Keywords

  • Blow-up rate
  • Global and local existence
  • Keller-Segel system
  • Weak L-L estimate

ASJC Scopus subject areas

  • Mathematics(all)

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