Open AccessStochastic dynamics of non-autonomous fractional Ginzburg-Landau equations on $ \mathbb{R}^3 $
Author(s) -
H. Peter Lu,
Ji Li,
Mingji Zhang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022028
Subject(s) - mathematics , uniqueness , attractor , pullback attractor , compact space , pullback , multiplicative function , dissipative system , semigroup , pure mathematics , mathematical physics , mathematical analysis , physics , quantum mechanics
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 \begin{document}$ L^2( \mathbb{R}^3) $\end{document} . The existence and uniqueness of tempered pullback attractors for the cocycle under certain dissipative conditions is then established. The periodicity of the tempered attractors is also proved when the deterministic non-autonomous external terms are periodic in time. The pullback asymptotic compactness of the cocycle in \begin{document}$ L^2( \mathbb{R}^3) $\end{document} is established by the uniform estimates on the tails of solutions for sufficiently large space and time variables.