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*

*この研究の対応する著者

研究成果: Article査読

13 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)732-751
ページ数20
ジャーナルMathematische Nachrichten
283
5
DOI
出版ステータスPublished - 2010 5 1
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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