# American Institute of Mathematical Sciences

May  2021, 20(5): 1907-1930. doi: 10.3934/cpaa.2021052

## Dynamics of a 3D Brinkman-Forchheimer equation with infinite delay

 1 Faculty of Science, Beijing University of Technology, Ping Le Yuan 100, Chaoyang District, Beijing, 100124, China 2 Department of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

* Corresponding author: Rong Yang

Received  October 2020 Revised  January 2021 Published  May 2021 Early access  March 2021

Fund Project: R. Yang is partially supported by NSFC (No. 11601021). X.-G. Yang is partially supported by the Fund of Young Backbone Teacher in Henan Province (No. 2018GGJS039), Incubation Fund from Henan Normal University (No. 2020PL17) and Henan Overseas Expertise Introduction Center for Discipline Innovation (No. CXJD2020003)

This paper is concerned with the pullback dynamics and asymptotic stability for a 3D Brinkman-Forchheimer equation with infinite delay. The well-posedness of weak solution to the 3D Brinkman-Forchheimer flow with infinite delay is investigated in the weighted space $C_\kappa(H)$ firstly, then the pullback attractors are presented for the process of weak solution. Moreover, the existence of global attractor and the exponential stability analysis of stationary solutions are shown, which is based on the estimate of corresponding steady state equation.

Citation: Wenjing Liu, Rong Yang, Xin-Guang Yang. Dynamics of a 3D Brinkman-Forchheimer equation with infinite delay. Communications on Pure & Applied Analysis, 2021, 20 (5) : 1907-1930. doi: 10.3934/cpaa.2021052
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