PULLBACK DYNAMICS OF A 3D MODIFIED NAVIER-STOKES EQUATIONS WITH DOUBLE DELAYS

被引：2

作者：

Zhang, Pan ^{[1
]}

Huang, Lan ^{[1
]}

Lu, Rui ^{[2
]}

Yang, Xin-Guang ^{[3
]}

机构：

[1] North China Univ Water Resources & Elect Power, Coll Math & Stat, Zhengzhou 450011, Peoples R China

[2] China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China

[3] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

来源：

ELECTRONIC RESEARCH ARCHIVE | 2021年 / 29卷 / 06期

基金：

中国国家自然科学基金;

关键词：

3D modified Navier-Stokes equations; double delays; tempered pullback attractors; BRINKMAN-FORCHHEIMER EQUATION; ASYMPTOTIC-BEHAVIOR; ATTRACTORS; STABILITY; EXISTENCE; MODELS; DECAY;

D O I：

10.3934/era.2021076

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the tempered pullback dynamics for a 3D modified Navier-Stokes equations with double time-delays, which includes delays on external force and convective terms respectively. Based on the property of monotone operator and some suitable hypotheses on the external forces, the existence and uniqueness of weak solutions can be shown in an appropriate functional Banach space. By using the energy equation technique and weak convergence method to achieve asymptotic compactness for the process, the existence of minimal family of pullback attractors has also been derived.

引用

页码：4137 / 4157

页数：21

共 41 条

[1]

[Anonymous], 1969, Quelques mthodes de rsolution des problmes aux limites non linaires

[2] EXISTENCE AND ANALYTICITY OF LEI-LIN SOLUTION TO THE NAVIER-STOKES EQUATIONS [J].

Bae, Hantaek .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143 (07) :2887-2892

[3]

Ball JM, 2004, DISCRETE CONT DYN-A, V10, P31

[4] Nonuniqueness of weak solutions to the Navier-Stokes equation [J].

Buckmaster, Tristan ;

Vicol, Vlad .

ANNALS OF MATHEMATICS, 2019, 189 (01) :101-144

[5] Attractors for 2D-Navier-Stokes models with delays [J].

Caraballo, T ;

Real, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 205 (02) :271-297

[6] Asymptotic behaviour of two-dimensional Navier-Stokes equations with delays [J].

Caraballo, T ;

Real, J .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2003, 459 (2040) :3181-3194

[7] Navier-Stokes equations with delays [J].

Caraballo, T ;

Real, J .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2014) :2441-2453

[8] A SURVEY ON NAVIER-STOKES MODELS WITH DELAYS: EXISTENCE, UNIQUENESS AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS [J].

Caraballo, Tomas ;

Han, Xiaoying .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2015, 8 (06) :1079-1101

[9] THREE-DIMENSIONAL SYSTEM OF GLOBALLY MODIFIED NAVIER-STOKES EQUATIONS WITH DELAY [J].

Caraballo, Tomas ;

Real, Jose ;

Marquez, Antonio M. .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2010, 20 (09) :2869-2883

[10] The long-time dynamics of 3D non-autonomous Navier-Stokes equations with variable viscosity [J].

Chen, Yongqiang ;

Yang, Xin-Guang ;

Si, Mengmeng .

SCIENCEASIA, 2018, 44 (01) :18-26

← 1 2 3 4 5 →