Pullback dynamics of a 3D modified Navier-Stokes equations with double delays

Pan Zhang; Lan Huang; Rui Lu; Xin-Guang Yang; Pan Zhang; Lan Huang; Rui Lu; Xin-Guang Yang

doi:10.3934/era.2021076

Electronic Research Archive

2021, Volume 29, Issue 6: 4137-4157. doi: 10.3934/era.2021076

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Pullback dynamics of a 3D modified Navier-Stokes equations with double delays

Pan Zhang ^{1
,},
Lan Huang ^{1
,
,},
Rui Lu ^{2
,},
Xin-Guang Yang ^{3
,}

1.
College of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
2.
Department of Mathematics, China University of Mining and Technology, Beijing 100083, China
3.
College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

Received: 01 May 2021 Revised: 01 July 2021 Published: 08 October 2021
35Q30, 35B40, 35B41, 76D03, 76D05

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.
- 3D modified Navier-Stokes equations,
- double delays,
- tempered pullback attractors
Citation: Pan Zhang, Lan Huang, Rui Lu, Xin-Guang Yang. Pullback dynamics of a 3D modified Navier-Stokes equations with double delays[J]. Electronic Research Archive, 2021, 29(6): 4137-4157. doi: 10.3934/era.2021076

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Abstract

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.

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