This work is concerned with the random dynamics of two-dimensional stochastic Boussinesq system with dynamical boundary condition. The white noises affect the system through a dynamical boundary condition. Using a method based on the theory of omega-limit compactness of a random dynamical system, we prove that the -random attractor for the generated random dynamical system is exactly the -random attractor. This improves a recent conclusion derived by Brune et al. on the existence of the -random attractor for the same system.
"-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions." Abstr. Appl. Anal. 2013 1 - 12, 2013. https://doi.org/10.1155/2013/706091