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 journalArticlepeer-review

    99 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 - Mar 1 2016

    All Science Journal Classification (ASJC) codes

    • Analysis

    Fingerprint

    Dive into the research topics of 'Existence and uniqueness theorem on mild solutions to the Keller-Segel system coupled with the Navier-Stokes fluid'. Together they form a unique fingerprint.

    Cite this