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

Hideo Kozono

doi:10.1006/jfan.2000.3625

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

Hideo Kozono^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

29 Citations (Scopus)

Abstract

Consider weak solutions w of the Navier-Stokes equations in Serrin's class w∈L^α(0, ∞; L^q(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 language	English
Pages (from-to)	153-197
Number of pages	45
Journal	Journal of Functional Analysis
Volume	176
Issue number	2
DOIs	https://doi.org/10.1006/jfan.2000.3625
Publication status	Published - 2000 Oct 1
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Analysis

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10.1006/jfan.2000.3625

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title = "Asymptotic Stability of Large Solutions with Large Perturbation to the Navier-Stokes Equations",

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 33. 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→∞.",

keywords = "Asymptotic stability, Energy inequality, L-L-estimates, Serrin's class",

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AU - Kozono, Hideo

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N2 - 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 33. 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→∞.

AB - 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 33. 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→∞.

KW - Asymptotic stability

KW - Energy inequality

KW - L-L-estimates

KW - Serrin's class

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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