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

Hideo Kozono, Masanari Miura, Yoshie Sugiyama

    研究成果: Article

    45 引用 (Scopus)

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    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.

    元の言語English
    ページ(範囲)1663-1683
    ページ数21
    ジャーナルJournal of Functional Analysis
    270
    発行部数5
    DOI
    出版物ステータスPublished - 2016 3 1

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    ASJC Scopus subject areas

    • Analysis

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