Decay rate of solutions to 3D Navier-Stokes-Voigt equations in Hm spaces

被引：16

作者：

Cung The Anh ^{[1
]}

Pham Thi Trang ^{[1
]}

机构：

[1] Hanoi Natl Univ Educ, Dept Math, 136 Xuan Thuy, Hanoi, Vietnam

来源：

APPLIED MATHEMATICS LETTERS | 2016年 / 61卷

关键词：

Navier-Stokes-Voigt equations; Decay rate; Fourier Splitting Method; Inductive argument; LARGE TIME BEHAVIOR; ATTRACTORS;

D O I：

10.1016/j.aml.2016.04.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first prove the regularity in H-m(R-3) of weak solutions to the Navier-Stokes-Voigt equations with initial data in H-K (R-3) for all m <= K. Then we compute the upper bound of decay rate for these solutions, specifically, we prove that parallel to del(m)(u)(t)parallel to(2) + parallel to del(m+1)(u)(t)parallel to(2) <= c(1+t)(-3/2-m), for large t, when u(0) is an element of H-sigma(m+1)(R-3) boolean AND L-1(R-3), m is an element of N. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：1 / 7

页数：7

共 11 条

[1] On questions of decay and existence for the viscous Camassa-Holm equations [J].

Bjorland, Clayton ;

Schonbek, Maria E. .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (05) :907-936

[2]

Cao YP, 2006, COMMUN MATH SCI, V4, P823

[3] Pull-back attractors for three-dimensional Navier-Stokes-Voigt equations in some unbounded domains [J].

Cung The Anh ;

Pham Thi Trang .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2013, 143 (02) :223-251

[4] Pullback attractors for three-dimensional non-autonomous Navier-Stokes-Voigt equations [J].

Garcia-Luengo, Julia ;

Marin-Rubio, Pedro ;

Real, Jose .

NONLINEARITY, 2012, 25 (04) :905-930

[5] Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations [J].

Kalantarov, Varga K. ;

Titi, Edriss S. .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2009, 30 (06) :697-714

[6] Decay characterization of solutions to Navier-Stokes-Voigt equations in terms of the initial datum [J].

Niche, Cesar J. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (05) :4440-4453

[7]

Oskolkov A. P., 1973, ZAP NAUCN SEM LENING, V38, P98, DOI DOI 10.1007/BF01084613

[8] LARGE TIME BEHAVIOR OF SOLUTIONS TO THE NAVIER-STOKES EQUATIONS [J].

SCHONBEK, ME .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1986, 11 (07) :733-763

[9] LARGE TIME BEHAVIOR OF SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN H-M SPACES [J].

SCHONBEK, ME .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1995, 20 (1-2) :103-117

[10] ATTRACTORS FOR AUTONOMOUS AND NONAUTONOMOUS 3D NAVIER-STOKES-VOIGHT EQUATIONS [J].

Yue, Gaocheng ;

Zhong, Chengkui .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2011, 16 (03) :985-1002

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