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

研究成果: Contribution to journalArticle査読

12 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.

本文言語英語
ページ(範囲)732-751
ページ数20
ジャーナルMathematische Nachrichten
283
5
DOI
出版ステータス出版済み - 5 1 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

フィンガープリント 「Strong solutions to the Keller-Segel system with the weak L <sup>n</sup><sub>2</sub> initial data and its application to the blow-up rate」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

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