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 $f
\in L^2_b(\mathbb{R};
H^{-1}(\Omega))$ is only translation bounded
instead of translation compact. The results in this paper will extend
and improve some results in Yue, Wang (Comput. Math. Appl., 2020) in the
case of non-autonomous and contain memory kernels which have not been
studied before.