The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations

We study the stability issue of the generalized 3D Navier-Stokes equations. It is shown that if the weak solution u of the Navier-Stokes equations lies in the regular class ∇u∈Lp(0,∞;Bq,∞0(ℝ3)), (2α/p)+(3/q)=2α, 2<q<∞, 0<α<1, then every weak solution v(x,t) of the perturbed system conver...

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Main Authors: Wen-Juan Wang, Yan Jia
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/321427
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author Wen-Juan Wang
Yan Jia
author_facet Wen-Juan Wang
Yan Jia
author_sort Wen-Juan Wang
collection DOAJ
description We study the stability issue of the generalized 3D Navier-Stokes equations. It is shown that if the weak solution u of the Navier-Stokes equations lies in the regular class ∇u∈Lp(0,∞;Bq,∞0(ℝ3)), (2α/p)+(3/q)=2α, 2<q<∞, 0<α<1, then every weak solution v(x,t) of the perturbed system converges asymptotically to u(x,t) as vt-utL2→0, t→∞.
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institution Kabale University
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publishDate 2013-01-01
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spelling doaj-art-6a944c0f153b469cafb6bc4f1dc2d65b2025-08-20T03:33:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/321427321427The Asymptotic Stability of the Generalized 3D Navier-Stokes EquationsWen-Juan Wang0Yan Jia1School of Mathematical Sciences, Anhui University, Hefei 230601, ChinaSchool of Mathematical Sciences, Anhui University, Hefei 230601, ChinaWe study the stability issue of the generalized 3D Navier-Stokes equations. It is shown that if the weak solution u of the Navier-Stokes equations lies in the regular class ∇u∈Lp(0,∞;Bq,∞0(ℝ3)), (2α/p)+(3/q)=2α, 2<q<∞, 0<α<1, then every weak solution v(x,t) of the perturbed system converges asymptotically to u(x,t) as vt-utL2→0, t→∞.http://dx.doi.org/10.1155/2013/321427
spellingShingle Wen-Juan Wang
Yan Jia
The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations
Journal of Applied Mathematics
title The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations
title_full The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations
title_fullStr The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations
title_full_unstemmed The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations
title_short The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations
title_sort asymptotic stability of the generalized 3d navier stokes equations
url http://dx.doi.org/10.1155/2013/321427
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