Abstract
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 theL2-random attractor for the generated random dynamical system is exactly theH1-random attractor. This improves a recent conclusion derived by Brune et al. on the existence of theL2-random attractor for the same system.
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