The Keller-Segel system of parabolic-parabolic type with initial data in weak Ln/2(ℝn) and its application to self-similar solutions

Hideo Kozono, Yoshie Sugiyama

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

We shall show the existence of a global strong solution to the semilinear Keller-Segel system in ℝn, n ≥ 3 of parabolic-parabolic type with small initial data u0 ∈ Lwn/2 (ℝn) and v0 ∈ BMO. Our method is based on the perturbation of linearization together with the Lp -L q-estimates of the heat semigroup and the fractional powers of the Laplace operator. As a by-product of our method, we shall construct a self-similar solution and prove the smoothing effect. Furthermore, the stability problem on our strong solutions will be also discussed.

Original languageEnglish
Pages (from-to)1467-1500
Number of pages34
JournalIndiana University Mathematics Journal
Volume57
Issue number4
DOIs
Publication statusPublished - 2008 Oct 22
Externally publishedYes

Keywords

  • BMO space
  • Heat semigroup
  • Keller-Segel system
  • Self-similar solution
  • Weak L -space

ASJC Scopus subject areas

  • Mathematics(all)

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