Stability of stationary solutions to the Navier–Stokes equations in the Besov space

Hideo Kozono*, Senjo Shimizu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We consider the stability of the stationary solution w of the Navier–Stokes equations in the whole space (Formula presented.) for (Formula presented.). It is clarified that if w is small in (Formula presented.) for (Formula presented.) and (Formula presented.), then for every small initial disturbance (Formula presented.) with (Formula presented.) and (Formula presented.) ((Formula presented.)), there exists a unique solution (Formula presented.) of the nonstationary Navier–Stokes equations on (0, ∞) with (Formula presented.) such that (Formula presented.) and (Formula presented.) as (Formula presented.), for (Formula presented.), (Formula presented.), and small (Formula presented.).

Original languageEnglish
Pages (from-to)1964-1982
Number of pages19
JournalMathematische Nachrichten
Volume296
Issue number5
DOIs
Publication statusPublished - 2023 May

Keywords

  • Navier–Stokes equations
  • homogeneous Besov space
  • stability
  • stationary solution

ASJC Scopus subject areas

  • General Mathematics

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