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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 706091, 12 pages
http://dx.doi.org/10.1155/2013/706091
Research Article

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

School of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received 24 August 2013; Accepted 25 October 2013

Academic Editor: Grzegorz Lukaszewicz

Copyright © 2013 Yijin Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 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.