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

    7 Citations (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

    Keywords

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

    ASJC Scopus subject areas

    • Analysis

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