THEORETICAL RESULTS ON THE EXISTENCE, REGULARITY AND ASYMPTOTIC STABILITY OF ENHANCED PULLBACK ATTRACTORS: APPLICATIONS TO 3D PRIMITIVE EQUATIONS*

doi:10.1007/s10473-023-0611-8

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2493-2518.doi: 10.1007/s10473-023-0611-8

THEORETICAL RESULTS ON THE EXISTENCE, REGULARITY AND ASYMPTOTIC STABILITY OF ENHANCED PULLBACK ATTRACTORS: APPLICATIONS TO 3D PRIMITIVE EQUATIONS^*

Renhai WANG¹, Boling GUO², Daiwen HUANG^2,†

1. School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, China;
2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

收稿日期:2022-06-08 修回日期:2023-06-06 发布日期:2023-12-08
通讯作者: †Daiwen HUANG, E-mail: hdw55@tom.com
作者简介:Renhai WANG, E-mail: rwang-math@outlook.com; Boling GUO, E-mail: gbl@iapcm.ac.cn
基金资助:
Wang's research was supported by China Postdoctoral Science Foundation (2020TQ0053 and 2020M680456),the research funds of Qianshixinmiao [2022]B16, Qianjiaoji [2022]124 and Qiankehepingtairencai-YSZ [2022]022. Guo's research was supported by the NSFC (11731014 and 11571254). Huang's research was partially supported by the NSFC (11971067, 11631008, 11771183).

THEORETICAL RESULTS ON THE EXISTENCE, REGULARITY AND ASYMPTOTIC STABILITY OF ENHANCED PULLBACK ATTRACTORS: APPLICATIONS TO 3D PRIMITIVE EQUATIONS^*

Renhai WANG¹, Boling GUO², Daiwen HUANG^2,†

1. School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, China;
2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2022-06-08 Revised:2023-06-06 Published:2023-12-08
Contact: †Daiwen HUANG, E-mail: hdw55@tom.com
About author:Renhai WANG, E-mail: rwang-math@outlook.com; Boling GUO, E-mail: gbl@iapcm.ac.cn
Supported by:
Wang's research was supported by China Postdoctoral Science Foundation (2020TQ0053 and 2020M680456),the research funds of Qianshixinmiao [2022]B16, Qianjiaoji [2022]124 and Qiankehepingtairencai-YSZ [2022]022. Guo's research was supported by the NSFC (11731014 and 11571254). Huang's research was partially supported by the NSFC (11971067, 11631008, 11771183).

摘要/Abstract

摘要： Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies. Then we provide some theoretical results for the existence, regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs. The existence of these enhanced attractors is harder to obtain than the backward case [33], since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval. As applications of our theoretical results, we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics, and prove the existence, regularity and asymptotic stability of the enhanced pullback attractors in $V\times V$ and $H^2\times H^2$ for the time-dependent forces which satisfy some weak conditions.

关键词: 3D primitive equations, pullback attractors, regularity, flattening, stability

Abstract: Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies. Then we provide some theoretical results for the existence, regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs. The existence of these enhanced attractors is harder to obtain than the backward case [33], since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval. As applications of our theoretical results, we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics, and prove the existence, regularity and asymptotic stability of the enhanced pullback attractors in $V\times V$ and $H^2\times H^2$ for the time-dependent forces which satisfy some weak conditions.

Key words: 3D primitive equations, pullback attractors, regularity, flattening, stability

中图分类号:

35Q35

Renhai WANG, Boling GUO, Daiwen HUANG. THEORETICAL RESULTS ON THE EXISTENCE, REGULARITY AND ASYMPTOTIC STABILITY OF ENHANCED PULLBACK ATTRACTORS: APPLICATIONS TO 3D PRIMITIVE EQUATIONS^*[J]. 数学物理学报(英文版), 2023, 43(6): 2493-2518.

Renhai WANG, Boling GUO, Daiwen HUANG. THEORETICAL RESULTS ON THE EXISTENCE, REGULARITY AND ASYMPTOTIC STABILITY OF ENHANCED PULLBACK ATTRACTORS: APPLICATIONS TO 3D PRIMITIVE EQUATIONS^*[J]. Acta mathematica scientia,Series B, 2023, 43(6): 2493-2518.

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THEORETICAL RESULTS ON THE EXISTENCE, REGULARITY AND ASYMPTOTIC STABILITY OF ENHANCED PULLBACK ATTRACTORS: APPLICATIONS TO 3D PRIMITIVE EQUATIONS^*

THEORETICAL RESULTS ON THE EXISTENCE, REGULARITY AND ASYMPTOTIC STABILITY OF ENHANCED PULLBACK ATTRACTORS: APPLICATIONS TO 3D PRIMITIVE EQUATIONS^*

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