Strong solutions to the Keller-Segel system with the weak L n 2 initial data and its application to the blow-up rate

Hideo Kozono, Yoshie Sugiyama

Research output: Contribution to journalArticle

12 Citations (Scopus)


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 n 2w (Rn), the weak L n 2 -space on Rn. If ||u0||L n 2 w (Rn) is sufficiently small, then our solution exists globally in time. Our motivation to construct solutions in L n 2w (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
Issue number5
Publication statusPublished - 2010 May
Externally publishedYes



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

ASJC Scopus subject areas

  • Mathematics(all)

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