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

Wenjing Liu; Rong Yang; Xin-Guang Yang

doi:10.3934/cpaa.2021052

Article Contents

2021, Volume 20, Issue 5: 1907-1930. Doi: 10.3934/cpaa.2021052

This issue Previous Article Forward-backward approximation of nonlinear semigroups in finite and infinite horizon Next Article Existence of large-data global weak solutions to a model of a strain-limiting viscoelastic body

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
^* Corresponding author: Rong Yang

Received: October 2020

Revised: January 2021

Early access: March 22, 2021

Published online: March 22, 2021

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)

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q30, 35B40, 35B41; Secondary: 35Q35, 76D05.

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