Asymptotically autonomous dynamics for non-autonomous stochastic $ g $-Navier-Stokes equation with additive noise

Abstract

<p style='text-indent:20px;'>Both sufficient and necessary criteria for the existence of a bi-parametric attractor which attaches with forward compactness is established. Meanwhile, we prove that, under certain conditions, the components of the random attractor of a non-autonomous dynamical system can converge in time to those of the random attractor of the limiting autonomous dynamical system. As an application of the abstract theory, we show that the non-autonomous stochastic <inline-formula><tex-math id="M2">\begin{document}$ g $\end{document}</tex-math></inline-formula>-Navier-Stokes (g-NS) equation possesses a forward compact random attractor such that it is forward asymptotically autonomous to a random attractor of the autonomous g-NS equation.</p>