Existence and uniqueness theorem on mild solutions to the Keller-Segel system coupled with the Navier-Stokes fluid

Hideo Kozono, Masanari Miura, Yoshie Sugiyama

    Research output: Contribution to journalArticle

    31 Citations (Scopus)

    Abstract

    We consider the Keller-Segel system coupled with the Navier-Stokes fluid in the whole space, and prove the existence of global mild solutions with the small initial data in the scaling invariant space. Our method is based on the implicit function theorem which yields necessarily continuous dependence of solutions for the initial data. As a byproduct, we show the asymptotic stability of solutions as the time goes to infinity. Since we may deal with the initial data in the weak Lp-spaces, the existence of self-similar solutions provided the initial data are small homogeneous functions.

    Original languageEnglish
    Pages (from-to)1663-1683
    Number of pages21
    JournalJournal of Functional Analysis
    Volume270
    Issue number5
    DOIs
    Publication statusPublished - 2016 Mar 1

    Fingerprint

    Existence and Uniqueness Theorem
    Mild Solution
    Navier-Stokes
    Coupled System
    Fluid
    Small Function
    Homogeneous Function
    Implicit Function Theorem
    Self-similar Solutions
    Stability of Solutions
    Continuous Dependence
    Lp Spaces
    Asymptotic Stability
    Infinity
    Scaling
    Invariant

    Keywords

    • Asymptotic stability
    • Continuous dependence for the initial data
    • Existence of global mild solutions
    • Keller-Segel system
    • Navier-Stokes equations
    • Self-similar solutions

    ASJC Scopus subject areas

    • Analysis

    Cite this

    Existence and uniqueness theorem on mild solutions to the Keller-Segel system coupled with the Navier-Stokes fluid. / Kozono, Hideo; Miura, Masanari; Sugiyama, Yoshie.

    In: Journal of Functional Analysis, Vol. 270, No. 5, 01.03.2016, p. 1663-1683.

    Research output: Contribution to journalArticle

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