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

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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 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
Issue number5
Publication statusPublished - May 1 2010


All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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