Existence and long‐time behavior of solutions to the velocity–vorticity–Voigt model of the 3D Navier–Stokes equations with damping and memory

Abstract

In this paper, we study the long-time dynamical behavior of the non-autonomous velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory. We first investigate the existence and uniqueness of weak solutions to the initial boundary value problem for above-mentioned model. Next, we prove the existence of uniform attractor of this problem, where the time-dependent forcing term 𝑓 ∈ L 2 b (R; H −1 (Ω)) is only translation bounded instead of translation compact. The results in this paper will extend and improve some results in Yue and Wang (Comput. Math. Appl., 2020) in the case of non-autonomous and contain memory kernels which have not been studied before.