Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations

This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estima...

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Main Author:	Junbai Ren
Format:	Article
Language:	English
Published:	Hindawi Limited 2014-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2014/879780

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spelling	doaj-0fec8077e00c4d8db171467d143dcc342020-11-24T23:59:50ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/879780879780Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes EquationsJunbai Ren0Research Center of Applied Statistics, School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaThis paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C1(1+t)-3/4≤uL2≤C2(1+t)-3/4, t>1. The decay rate is optimal since it coincides with that of heat equation.http://dx.doi.org/10.1155/2014/879780
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Junbai Ren
spellingShingle	Junbai Ren Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations Abstract and Applied Analysis
author_facet	Junbai Ren
author_sort	Junbai Ren
title	Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations
title_short	Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations
title_full	Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations
title_fullStr	Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations
title_full_unstemmed	Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations
title_sort	large time behavior for weak solutions of the 3d globally modified navier-stokes equations
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2014-01-01
description	This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C1(1+t)-3/4≤uL2≤C2(1+t)-3/4, t>1. The decay rate is optimal since it coincides with that of heat equation.
url	http://dx.doi.org/10.1155/2014/879780
work_keys_str_mv	AT junbairen largetimebehaviorforweaksolutionsofthe3dgloballymodifiednavierstokesequations
_version_	1725445975615471616

Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations

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