Singular limit problem for the Keller–Segel system and drift–diffusion system in scaling critical spaces

Masaki Kurokiba, Takayoshi Ogawa

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider a singular limit problem for the Cauchy problem of the Keller–Segel equation in a critical function space. We show that a solution to the Keller–Segel system in a scaling critical function space converges to a solution to the drift–diffusion system of parabolic–elliptic type (the simplified Keller–Segel model) in the critical space strongly as the relaxation time τ→ ∞. For the proof of singular limit problem, we employ generalized maximal regularity for the heat equation and use it systematically with the sequence of embeddings between the interpolation spaces B˙q,σs(Rn) and F˙q,σs(Rn).

Original languageEnglish
Pages (from-to)421-457
Number of pages37
JournalJournal of Evolution Equations
Volume20
Issue number2
DOIs
Publication statusPublished - 2020 Jun 1

Keywords

  • Critical space
  • Drift–diffusion system
  • Global well-posedness
  • Keller–Segel equation
  • Maximal regularity
  • Scaling invariance
  • Singular limit problem

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Fingerprint Dive into the research topics of 'Singular limit problem for the Keller–Segel system and drift–diffusion system in scaling critical spaces'. Together they form a unique fingerprint.

  • Cite this