Asymptotic behavior of stochastic g-Navier-Stokes equations on a sequence of expanding domains

The limiting dynamics of stochastic 2D nonautonomous g-Navier-Stokes equations defined on a sequence of expanding domains are investigated, where the limiting domain is unbounded. By generalizing the energy-equation method, we show that the sequence of expanding cocycles is weakly equicontinuous and strongly equiasymptotically compact, which lead to both existence and upper semicontinuity of the null-expansion of the corresponding random attractor when the bounded domain approaches to the unbounded domain.