Regular attractors of asymptotically autonomous stochastic 3D Brinkman-Forchheimer equations with delays

Qiangheng Zhang; Yangrong Li

doi:10.3934/cpaa.2021117

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2021, Volume 20, Issue 10: 3515-3537. Doi: 10.3934/cpaa.2021117 open access

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Regular attractors of asymptotically autonomous stochastic 3D Brinkman-Forchheimer equations with delays

Qiangheng Zhang and
Yangrong Li^,

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

^* Corresponding author
^* Corresponding author

Received: March 2021

Revised: June 2021

Early access: July 2021

Published: October 2021

This work was supported by the Natural Science Foundation of China Grant 11571283

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Abstract

We study asymptotically autonomous dynamics for non-autonom-ous stochastic 3D Brinkman-Forchheimer equations with general delays (containing variable delay and distributed delay). We first prove the existence of a pullback random attractor not only in the initial space but also in the regular space. We then prove that, under the topology of the regular space, the time-fibre of the pullback random attractor semi-converges to the random attractor of the autonomous stochastic equation as the time-parameter goes to minus infinity. The general delay force is assumed to be pointwise Lipschitz continuous only, which relaxes the uniform Lipschitz condition in the literature and includes more examples.

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Mathematics Subject Classification: Primary: 37L55; Secondary: 35B41, 35R60.

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