Stochastic dynamics of non-autonomous fractional Ginzburg-Landau equations on $ \mathbb{R}^3 $

Abstract

<p style='text-indent:20px;'>We investigate a class of non-autonomous non-local fractional stochastic Ginzburg-Landau equation with multiplicative white noise in three spatial dimensions. Of particular interest is the asymptotic behavior of its solutions. We first prove the pathwise well-posedness of the equation and define a continuous non-autonomous cocycle in <inline-formula><tex-math id="M2">\begin{document}$ L^2( \mathbb{R}^3) $\end{document}</tex-math></inline-formula>. The existence and uniqueness of tempered pullback attractors for the cocycle under certain dissipative conditions is then established. The periodicity of the tempered attractors is also proved when the deterministic non-autonomous external terms are periodic in time. The pullback asymptotic compactness of the cocycle in <inline-formula><tex-math id="M3">\begin{document}$ L^2( \mathbb{R}^3) $\end{document}</tex-math></inline-formula> is established by the uniform estimates on the tails of solutions for sufficiently large space and time variables.</p>