Navier-Stokes equations with external forces in time-weighted Besov spaces

Hideo Kozono, Senjo Shimizu

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    We show existence theorem of global mild solutions with small initial data and external forces in the time-weighted Besov space which is an invariant space under the change of scaling. The result on local existence of solutions for large data is also discussed. Our method is based on the Lp-Lq estimate of the Stokes equations in Besov spaces. Since we construct the global solution by means of the implicit function theorem, as a byproduct, its stability with respect to the given data is necessarily obtained.

    Original languageEnglish
    JournalMathematische Nachrichten
    DOIs
    Publication statusAccepted/In press - 2018 Jan 1

    Fingerprint

    Besov Spaces
    Weighted Spaces
    Navier-Stokes Equations
    Lp Estimates
    Implicit Function Theorem
    Local Existence
    Stokes Equations
    Mild Solution
    Large Data
    Global Solution
    Existence Theorem
    Existence of Solutions
    Scaling
    Invariant

    Keywords

    • 35Q30
    • 76D03
    • 76D05
    • Global well-posedness
    • Navier-Stokes equations
    • Singular data
    • Time-weighted Besov spaces

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Navier-Stokes equations with external forces in time-weighted Besov spaces. / Kozono, Hideo; Shimizu, Senjo.

    In: Mathematische Nachrichten, 01.01.2018.

    Research output: Contribution to journalArticle

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