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

    17 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

    Keywords

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

    ASJC Scopus subject areas

    • Analysis

    Fingerprint Dive into the research topics of 'A remark on Liouville-type theorems for the stationary Navier–Stokes equations in three space dimensions'. Together they form a unique fingerprint.

  • Cite this