Asymptotic Stability of Large Solutions with Large Perturbation to the Navier-Stokes Equations

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Abstract

Consider weak solutions w of the Navier-Stokes equations in Serrin's class w∈Lα(0, ∞; Lq(Ω)) for 2/α+3/q=1 with 3<q≤∞, where Ω is a general unbounded domain in R3. We shall show that although the initial and external disturbances from w are large, every perturbed flow v with the energy inequality converges asymptotically to w as v(t)-w(t)L2(Ω)→0, ∇v(t)-∇w(t)L2(Ω)=O(t-1/2) as t→∞.

Original languageEnglish
Pages (from-to)153-197
Number of pages45
JournalJournal of Functional Analysis
Volume176
Issue number2
DOIs
Publication statusPublished - 2000 Oct 1

Keywords

  • Asymptotic stability
  • Energy inequality
  • L-L-estimates
  • Serrin's class

ASJC Scopus subject areas

  • Analysis

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