Singular sensitivity in a Keller–Segel-fluid system

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Tobias Black
  • J. Lankeit
  • M. Mizukami

External Research Organisations

  • Paderborn University
  • Tokyo University of Science
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Details

Original languageEnglish
Pages (from-to)561-581
Number of pages21
JournalJournal of evolution equations
Volume18
Issue number2
Early online date28 Oct 2017
Publication statusPublished - Jun 2018
Externally publishedYes

Abstract

In bounded smooth domains Ω ⊂ R N, N∈ { 2 , 3 } , considering the chemotaxis–fluid system nt+u·∇n=Δn-χ∇·(nc∇c)ct+u·∇c=Δc-c+nut+κ(u·∇)u=Δu+∇P+n∇ϕ with singular sensitivity, we prove global existence of classical solutions for given ϕ∈ C 2(Ω ¯) , for κ= 0 (Stokes-fluid) if N= 3 and κ∈ { 0 , 1 } (Stokes- or Navier–Stokes-fluid) if N= 2 and under the condition that 0<χ<2N.

Keywords

    Chemotaxis–fluid, Global existence, Keller–Segel, Navier–Stokes, Singular sensitivity

ASJC Scopus subject areas

Cite this

Singular sensitivity in a Keller–Segel-fluid system. / Black, Tobias; Lankeit, J.; Mizukami, M.
In: Journal of evolution equations, Vol. 18, No. 2, 06.2018, p. 561-581.

Research output: Contribution to journal › Article › Research › peer review

Black T, Lankeit J, Mizukami M. Singular sensitivity in a Keller–Segel-fluid system. Journal of evolution equations. 2018 Jun;18(2):561-581. Epub 2017 Oct 28. doi: 10.1007/s00028-017-0411-5
Black, Tobias ; Lankeit, J. ; Mizukami, M. / Singular sensitivity in a Keller–Segel-fluid system. In: Journal of evolution equations. 2018 ; Vol. 18, No. 2. pp. 561-581.
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AU - Lankeit, J.

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