Global solvability of the Navier-Stokes equations with a free surface in the maximal Lp-Lq regularity class

Hirokazu Saito

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the N-dimensional Euclidean space for N≥2. The aim of this paper is to show the global solvability of the Navier-Stokes equations with a free surface, describing the above-mentioned motion, in the maximal Lp-Lq regularity class. Our approach is based on the maximal Lp-Lq regularity with exponential stability for the linearized equations, and also it is proved that solutions to the original nonlinear problem are exponentially stable.

    Original languageEnglish
    JournalJournal of Differential Equations
    DOIs
    Publication statusAccepted/In press - 2017

    Fingerprint

    Global Solvability
    Free Surface
    Navier Stokes equations
    Navier-Stokes Equations
    Regularity
    Motion
    Exponential Stability
    Viscous Fluid
    Incompressible Fluid
    Nonlinear Problem
    Euclidean space
    Asymptotic stability
    Fluids
    Class

    Keywords

    • Exponential stability
    • Free surfaces
    • Global solvability
    • Lp-Lq framework
    • Maximal regularity
    • Navier-Stokes equations
    • Primary
    • Secondary

    ASJC Scopus subject areas

    • Analysis

    Cite this

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    abstract = "We consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the N-dimensional Euclidean space for N≥2. The aim of this paper is to show the global solvability of the Navier-Stokes equations with a free surface, describing the above-mentioned motion, in the maximal Lp-Lq regularity class. Our approach is based on the maximal Lp-Lq regularity with exponential stability for the linearized equations, and also it is proved that solutions to the original nonlinear problem are exponentially stable.",
    keywords = "Exponential stability, Free surfaces, Global solvability, Lp-Lq framework, Maximal regularity, Navier-Stokes equations, Primary, Secondary",
    author = "Hirokazu Saito",
    year = "2017",
    doi = "10.1016/j.jde.2017.09.045",
    language = "English",
    journal = "Journal of Differential Equations",
    issn = "0022-0396",
    publisher = "Academic Press Inc.",

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    T1 - Global solvability of the Navier-Stokes equations with a free surface in the maximal Lp-Lq regularity class

    AU - Saito, Hirokazu

    PY - 2017

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    N2 - We consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the N-dimensional Euclidean space for N≥2. The aim of this paper is to show the global solvability of the Navier-Stokes equations with a free surface, describing the above-mentioned motion, in the maximal Lp-Lq regularity class. Our approach is based on the maximal Lp-Lq regularity with exponential stability for the linearized equations, and also it is proved that solutions to the original nonlinear problem are exponentially stable.

    AB - We consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the N-dimensional Euclidean space for N≥2. The aim of this paper is to show the global solvability of the Navier-Stokes equations with a free surface, describing the above-mentioned motion, in the maximal Lp-Lq regularity class. Our approach is based on the maximal Lp-Lq regularity with exponential stability for the linearized equations, and also it is proved that solutions to the original nonlinear problem are exponentially stable.

    KW - Exponential stability

    KW - Free surfaces

    KW - Global solvability

    KW - Lp-Lq framework

    KW - Maximal regularity

    KW - Navier-Stokes equations

    KW - Primary

    KW - Secondary

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    M3 - Article

    JO - Journal of Differential Equations

    JF - Journal of Differential Equations

    SN - 0022-0396

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