Forward dynamics of 3D double time-delayed MHD-Voight equations

Abstract

This paper is concerned with the long-term behaviour of 3D double time-delayed magnetohydrodynamics (MHD)-Voight equations with non-autonomous forcing term. First, we establish the existence, forward compactness and forward stability of pullback attractors by the forward equi-continuity and forward pullback asymptotic compactness of solutions. We then study the upper semi-convergence of pullback attractors as the time parameter tends to positive infinity. Since the solution of this equation has no high regularity, we use the spectrum decomposition technique to prove the forward pointwise pullback asymptotic compactness of solutions.

Keywords:

• MHD-Voight equations
• delay
• pullback attractor
• time-dependent property
• spectrum decomposition

2020 Mathematics Subject Classifications:

• 35B40
• 35B41
• 37L05
• 34K20

Acknowledgments

The authors would like to express their sincere thanks to the referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statements

All data generated or analysed during this study are included in this manuscript.

Additional information

Funding

Zhang was supported by Shandong Provincial Natural Science Foundation [grant number ZR2022QA054].