Random attractors for non-autonomous stochastic Brinkman-Forchheimer equations on unbounded domains

Shu Wang; Mengmeng Si; Rong Yang

doi:10.3934/cpaa.2022034

Article Contents

2022, Volume 21, Issue 5: 1621-1636. Doi: 10.3934/cpaa.2022034

This issue Previous Article Global behavior for the classical solution of compressible viscous micropolar fluid with cylinder symmetry Next Article Monotonicity and nonexistence of positive solutions for pseudo-relativistic equation with indefinite nonlinearity

Random attractors for non-autonomous stochastic Brinkman-Forchheimer equations on unbounded domains

Faculty of Sciences, Beijing University of Technology, PingLeYuan 100, Chaoyang District, Beijing 100124, China

^* Corresponding author
^* Corresponding author

Received: November 30, 2021

Revised: December 31, 2021

Early access: February 2022

Published: May 2022

The work is supported by National Natural Science Foundation of China (Nos.11601021, 11831003, 11771031, and 12171111), the Science and Technology Project of Beijing Municipal Education Commission(No.KZ202110005011), and Project for University Key Young Teacher by Education of Henan Province (No.2021GGJS158)

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Abstract

In this paper, we study the asymptotic behavior of the non-autonomous stochastic 3D Brinkman-Forchheimer equations on unbounded domains. We first define a continuous non-autonomous cocycle for the stochastic equations, and then prove that the existence of tempered random attractors by Ball's idea of energy equations. Furthermore, we obtain that the tempered random attractors are periodic when the deterministic non-autonomous external term is periodic in time.

Keywords:

Stochastic Brinkman-Forchheimer equations,
non-autonomous,
unbounded domains,
random attractors.

Mathematics Subject Classification: Primary: 35Q30; Secondary: 35Q35, 37H10, 35B41.

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References

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