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

الملخص EN

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.