A remark on Liouville-type theorems for the stationary Navier–Stokes equations in three space dimensions

Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    Consider the 3D homogeneous stationary Navier–Stokes equations in the whole space R3. We deal with solutions vanishing at infinity in the class of the finite Dirichlet integral. By means of quantities having the same scaling property as the Dirichlet integral, we establish new a priori estimates. As an application, we prove the Liouville theorem in the marginal case of scaling invariance.

    Original languageEnglish
    Pages (from-to)804-818
    Number of pages15
    JournalJournal of Functional Analysis
    Volume272
    Issue number2
    DOIs
    Publication statusPublished - 2017 Jan 15

    Fingerprint

    Dirichlet Integral
    Liouville Type Theorem
    Navier-Stokes Equations
    Scaling
    Liouville's theorem
    A Priori Estimates
    Invariance
    Infinity
    Class

    Keywords

    • Finite Dirichlet integral
    • Liouville-type theorem
    • Navier–Stokes equations
    • Scaling invariance

    ASJC Scopus subject areas

    • Analysis

    Cite this

    A remark on Liouville-type theorems for the stationary Navier–Stokes equations in three space dimensions. / Kozono, Hideo; Terasawa, Yutaka; Wakasugi, Yuta.

    In: Journal of Functional Analysis, Vol. 272, No. 2, 15.01.2017, p. 804-818.

    Research output: Contribution to journalArticle

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