Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces

Hideo Kozono, Yoshie Sugiyama

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

We shall show existence of global strong solution to the semi-linear Keller-Segel system in Rn, n ≥ 3, of parabolic-parabolic type with small initial data u0 ∈ Hfrac(n, r) - 2, r (Rn) and v0 ∈ Hfrac(n, r), r (Rn) for max {1, n / 4} < r < n / 2. Our method is based on the perturbation of linealization together with the Lp-Lq estimates of the heat semigroup and the fractional powers of the Laplace operator. As a by-product of our method, we shall prove the decay property of solutions as the time goes to infinity.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalJournal of Differential Equations
Volume247
Issue number1
DOIs
Publication statusPublished - 2009 Jul 1
Externally publishedYes

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Scale Invariant
Strong Solution
Semilinear
Byproducts
Heat Semigroup
Lp Estimates
Fractional Powers
Laplace Operator
Infinity
Decay
Perturbation
Hot Temperature

ASJC Scopus subject areas

  • Analysis

Cite this

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