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Regular Dynamics for 3D Brinkman–Forchheimer Equations with Delays

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Abstract

The aim of this paper is to study the regular dynamics for the 3D delay Brinkman–Forchheimer (BF) equations. We first prove the existence, uniqueness and time-dependent property of regular tempered pullback attractors as well as the existence of invariant measures for the 3D BF equations with non-autonomous abstract delay. We then study the asymptotic autonomy of regular pullback attractors for the 3D BF equations with autonomous abstract delay. Finally, we discuss the upper semicontinuity of regular pullback attractors as the delay time approaches to zero for the 3D BF equations with variable delay and distributed delay.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Heze University, Heze, 274015, China

    Qiangheng Zhang

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  1. Qiangheng Zhang
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Correspondence to Qiangheng Zhang.

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Communicated by Yong Zhou.

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Zhang, Q. Regular Dynamics for 3D Brinkman–Forchheimer Equations with Delays. Bull. Malays. Math. Sci. Soc. 45, 2959–2995 (2022). https://doi.org/10.1007/s40840-022-01315-y

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  • DOI: https://doi.org/10.1007/s40840-022-01315-y

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