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Journal of Function Spaces
Volume 2015, Article ID 303025, 6 pages
http://dx.doi.org/10.1155/2015/303025
Research Article

Blow-Up Criterion of Weak Solutions for the 3D Boussinesq Equations

1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2College of Information Science, Henan University of Technology, Zhengzhou 450001, China
3College of Education and Teacher Development, Henan Normal University, Xinxiang 453007, China
4High School Attached to HNU, Henan Normal University, Xinxiang 453007, China

Received 1 July 2014; Accepted 17 September 2014

Academic Editor: Józef Banaś

Copyright © 2015 Zhaohui Dai 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

The Boussinesq equations describe the three-dimensional incompressible fluid moving under the gravity and the earth rotation which come from atmospheric or oceanographic turbulence where rotation and stratification play an important role. In this paper, we investigate the Cauchy problem of the three-dimensional incompressible Boussinesq equations. By commutator estimate, some interpolation inequality, and embedding theorem, we establish a blow-up criterion of weak solutions in terms of the pressure in the homogeneous Besov space .