In this paper a nonautonomous dynamical system is considered, a stochastic one that is obtained from the dissipative Euler equation subject to a stochastic perturbation, an additive noise. Absorbing sets have been defined as sets that depend on time and attracts from $-\infty$. A stochastic weak attractor is constructed in phase space with respect to two metrics and is compact in the lower one.
Hakima Bessaih. "Stochastic Weak Attractor for a Dissipative Euler Equation." Electron. J. Probab. 5 1 - 16, 2000. https://doi.org/10.1214/EJP.v5-59