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

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

doi:10.3934/era.2021076

Article Contents

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

This issue Previous Article Accelerating reinforcement learning with a Directional-Gaussian-Smoothing evolution strategy Next Article Global dynamics of some system of second-order difference equations

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

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

^* Corresponding author: Lan Huang
^* Corresponding author: Lan Huang

Received: April 30, 2021

Revised: June 30, 2021

Early access: October 2021

Published: July 2021

Research partly supported by the NSFC (No. 11501199 and No. 11871212) and the Young Key Teachers Project in Higher Vocational Colleges of Henan Province (No. 2020GZGG109)

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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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Mathematics Subject Classification: 35Q30, 35B40, 35B41, 76D03, 76D05.

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