Abstract and Applied Analysis
Volume 2013 (2013), Article ID 653160, 10 pages
http://dx.doi.org/10.1155/2013/653160
Research Article

Random Dynamics of the Stochastic Boussinesq Equations Driven by Lévy Noises

Jianhua Huang,1 Yuhong Li,2 and Jinqiao Duan3

1Department of Mathematics, National University of Defense Technology, Changsha 410073, China
2College of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
3Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA

Received 13 December 2012; Accepted 17 January 2013

Academic Editor: Chuangxia Huang

Copyright © 2013 Jianhua Huang et al. 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 paper is devoted to the investigation of random dynamics of the stochastic Boussinesq equations driven by Lévy noise. Some fundamental properties of a subordinator Lévy process and the stochastic integral with respect to a Lévy process are discussed, and then the existence, uniqueness, regularity, and the random dynamical system generated by the stochastic Boussinesq equations are established. Finally, some discussions on the global weak solution of the stochastic Boussinesq equations driven by general Lévy noise are also presented.