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
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Analysis

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