Singular limit problem for the two-dimensional Keller-Segel system in scaling critical space

Masaki Kurokiba, Takayoshi Ogawa

Research output: Contribution to journalLetterpeer-review

1 Citation (Scopus)

Abstract

We consider the singular limit problem of the Cauchy problem to the Keller-Segel equation in the two dimensional critical space. It is shown that the solution to the Keller-Segel system in the scaling critical function space converges to the solution to the drift-diffusion system of parabolic-elliptic equations (the simplified Keller-Segel equation) in the critical space strongly as the relaxation time parameter τ→∞. For the proof, we show generalized maximal regularity for the heat equations and use it systematically with the sequence of embeddings between the interpolation spaces B˙q,σs(R2) and F˙q,σs(R2) for the proof of singular limit problem.

Original languageEnglish
Pages (from-to)8959-8997
Number of pages39
JournalJournal of Differential Equations
Volume269
Issue number10
DOIs
Publication statusPublished - 2020 Nov 5

Keywords

  • Bounded mean oscillation
  • Critical space
  • Drift-diffusion system
  • Keller-Segel equation
  • Maximal regularity
  • Singular limit problem

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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