Strong solutions of the Navier-Stokes equations with singular data

Hideo Kozono, Senjo Shimizu

    Research output: Chapter in Book/Report/Conference proceedingChapter

    1 Citation (Scopus)

    Abstract

    We construct strong solutions in the Serrin class of the Navier-Stokes equations with singular data. In 2D case, our results cover the initial vorticity as the Dirac measure and the external force whose support consists of a single point. In 3D case, we can handle the initial vortex sheet supported on the sphere and the singular external force whose support is concentrated on the surface.

    Original languageEnglish
    Title of host publicationContemporary Mathematics
    PublisherAmerican Mathematical Society
    Pages163-173
    Number of pages11
    Volume710
    DOIs
    Publication statusPublished - 2018 Jan 1

    Fingerprint

    Strong Solution
    Navier-Stokes Equations
    Vortex Sheet
    Vorticity
    Paul Adrien Maurice Dirac
    Cover
    Class

    Keywords

    • Dirac measure
    • Global strong solutions
    • Navier-Stokes equations
    • Single layer potential
    • Singular data

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Kozono, H., & Shimizu, S. (2018). Strong solutions of the Navier-Stokes equations with singular data. In Contemporary Mathematics (Vol. 710, pp. 163-173). American Mathematical Society. https://doi.org/10.1090/conm/710/14369

    Strong solutions of the Navier-Stokes equations with singular data. / Kozono, Hideo; Shimizu, Senjo.

    Contemporary Mathematics. Vol. 710 American Mathematical Society, 2018. p. 163-173.

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Kozono, H & Shimizu, S 2018, Strong solutions of the Navier-Stokes equations with singular data. in Contemporary Mathematics. vol. 710, American Mathematical Society, pp. 163-173. https://doi.org/10.1090/conm/710/14369
    Kozono H, Shimizu S. Strong solutions of the Navier-Stokes equations with singular data. In Contemporary Mathematics. Vol. 710. American Mathematical Society. 2018. p. 163-173 https://doi.org/10.1090/conm/710/14369
    Kozono, Hideo ; Shimizu, Senjo. / Strong solutions of the Navier-Stokes equations with singular data. Contemporary Mathematics. Vol. 710 American Mathematical Society, 2018. pp. 163-173
    @inbook{da1a3551f7bf4802b90f428c2811d511,
    title = "Strong solutions of the Navier-Stokes equations with singular data",
    abstract = "We construct strong solutions in the Serrin class of the Navier-Stokes equations with singular data. In 2D case, our results cover the initial vorticity as the Dirac measure and the external force whose support consists of a single point. In 3D case, we can handle the initial vortex sheet supported on the sphere and the singular external force whose support is concentrated on the surface.",
    keywords = "Dirac measure, Global strong solutions, Navier-Stokes equations, Single layer potential, Singular data",
    author = "Hideo Kozono and Senjo Shimizu",
    year = "2018",
    month = "1",
    day = "1",
    doi = "10.1090/conm/710/14369",
    language = "English",
    volume = "710",
    pages = "163--173",
    booktitle = "Contemporary Mathematics",
    publisher = "American Mathematical Society",
    address = "United States",

    }

    TY - CHAP

    T1 - Strong solutions of the Navier-Stokes equations with singular data

    AU - Kozono, Hideo

    AU - Shimizu, Senjo

    PY - 2018/1/1

    Y1 - 2018/1/1

    N2 - We construct strong solutions in the Serrin class of the Navier-Stokes equations with singular data. In 2D case, our results cover the initial vorticity as the Dirac measure and the external force whose support consists of a single point. In 3D case, we can handle the initial vortex sheet supported on the sphere and the singular external force whose support is concentrated on the surface.

    AB - We construct strong solutions in the Serrin class of the Navier-Stokes equations with singular data. In 2D case, our results cover the initial vorticity as the Dirac measure and the external force whose support consists of a single point. In 3D case, we can handle the initial vortex sheet supported on the sphere and the singular external force whose support is concentrated on the surface.

    KW - Dirac measure

    KW - Global strong solutions

    KW - Navier-Stokes equations

    KW - Single layer potential

    KW - Singular data

    UR - http://www.scopus.com/inward/record.url?scp=85050181344&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85050181344&partnerID=8YFLogxK

    U2 - 10.1090/conm/710/14369

    DO - 10.1090/conm/710/14369

    M3 - Chapter

    AN - SCOPUS:85050181344

    VL - 710

    SP - 163

    EP - 173

    BT - Contemporary Mathematics

    PB - American Mathematical Society

    ER -