Limiting dynamics of stochastic complex Ginzburg–Landau lattice systems with long-range interactions in weighted space

Abstract

This paper deals with the limiting dynamics of stochastic complex Ginzburg–Landau lattice systems with long-range interactions driven by nonlinear noise in a weighted space L2(Ω,lη2). We first consider the well-posedness of solutions for considered stochastic systems in the weighted space and then establish the existence and uniqueness of weak pullback mean random attractor in the weighted space.