End-point maximal regularity and its application to two-dimensional Keller-Segel system

Takayoshi Ogawa, Senjo Shimizu

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

We prove the maximal Lρ regularity of the Cauchy problem of the heat equation in the Besov space Ḃ10,ρ (ℝn) 1 > ρ ≤ ∞, which is not UMD space. And as its application, we establish the time local well-posedness of the solution of two dimensional nonlinear parabolic system with the Poisson equation in Ḃ10,2ℝ2), where the equation is considered in the space invariant by a scaling and particularly the natural free energy is well defined from the initial time. The small data global existence is also obtained in the same class.

Original languageEnglish
Pages (from-to)601-628
Number of pages28
JournalMathematische Zeitschrift
Volume264
Issue number3
DOIs
Publication statusPublished - 2010 Jan 1

ASJC Scopus subject areas

  • Mathematics(all)

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