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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 L2-random attractor for the generated random dynamical system is exactly the H1-random attractor. This improves a recent conclusion derived by Brune et al. on the existence of the L2-random attractor for the same system

abstract and applied analysis

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions

H1-Random Attractors and Asymptotic Smoothing Effect of Solutions for Stochastic Boussinesq Equations with Fluctuating Dynamical Boundary Conditions