Strong solutions of the Navier–Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces

Hideo Kozono, Senjo Shimizu

    Research output: Contribution to journalArticle

    2 Citations (Scopus)


    We show existence and uniqueness theorem of local strong solutions to the Navier–Stokes equations with arbitrary initial data and external forces in the homogeneous Besov space with both negative and positive differential orders which is an invariant space under the change of scaling. If the initial data and external forces are small, then the local solutions can be extended globally in time. Our solutions also belong to the Serrin class in the usual Lebesgue space. The method is based on the maximal Lorentz regularity theorem of the Stokes equations in the homogeneous Besov spaces. As an application, we may handle such singular data as the Dirac measure and the single layer potential supported on the sphere.

    Original languageEnglish
    JournalJournal of Functional Analysis
    Publication statusAccepted/In press - 2018 Jan 1



    • Homogeneous Besov space
    • Lorentz space
    • Maximal regularity
    • Navier–Stokes equations
    • Single layer potential

    ASJC Scopus subject areas

    • Analysis

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