Asymptotic behavior of non-autonomous stochastic complex Ginzburg-Landau equations on unbounded thin domains

This paper mainly investigates the asymptotic behavior of non-autonomous stochastic complex Ginzburg-Landau equations on unbounded thin domains. We first prove the existence and uniqueness of random attractors for the considered equation and its limit equation. Due to the non-compactness of Sobolev embeddings on unbounded domains, the pullback asymptotic compactness of such a stochastic equation is proved by the tail-estimate method. Then, we show the upper semi-continuity of random attractors when thin domains collapse onto the real space R.