About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 420721, 8 pages
http://dx.doi.org/10.1155/2012/420721
Research Article

Logarithmically Improved Regularity Criteria for a Fluid System with the Linear Soret Effect

1School of Mathematics and Information Science, Yantai University, Yantai 264005, China
2State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China

Received 27 July 2012; Accepted 21 August 2012

Academic Editor: Xinguang Zhang

Copyright © 2012 Minglei Zang and Xiaoyan Guan. 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.

Linked References

  1. B. Straughan, The Energy Method, Stability, and Nonlinear Convection, vol. 91, Springer, New York, NY, USA, 2ND edition, 2004.
  2. M. Malashetty, I. Pop, P. Kollur, and W. Sidrama, “Soret effect on double diffusive convection in a Darcy porous medium saturated with a couple stress fluid,” International Journal of Thermal Sciences, vol. 53, pp. 130–140, 2012.
  3. M. S. Malashetty, I. S. Shivakumara, and S. Kulkarni, “The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model,” Physics Letters A, vol. 373, no. 7, pp. 781–790, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. F. Xu and J. Yuan, “Global well-posedness for a fluid system with the linear Soret effect,” submitted.
  5. J. T. Beale, T. Kato, and A. Majda, “Remarks on the breakdown of smooth solutions for the 3-D Euler equations,” Communications in Mathematical Physics, vol. 94, no. 1, pp. 61–66, 1984. View at Publisher · View at Google Scholar
  6. H. Kozono and Y. Taniuchi, “Limiting case of the Sobolev inequality in BMO, with application to the Euler equations,” Communications in Mathematical Physics, vol. 214, no. 1, pp. 191–200, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J. Fan and Y. Zhou, “A note on regularity criterion for the 3D Boussinesq system with partial viscosity,” Applied Mathematics Letters, vol. 22, no. 5, pp. 802–805, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. C. H. Chan and A. Vasseur, “Log improvement of the Prodi-serrin criteria for Navier-Stokes equations,” Methods and Applications of Analysis, vol. 14, no. 2, pp. 197–212, 2007. View at Zentralblatt MATH
  9. Y. Zhou and Z. Lei, “Logarithmically improved regularity criterion for Euler and Navier-Stokes equations,” Preprint.
  10. H. Qiu, Y. Du, and Z. Yao, “Serrin-type blow-up criteria for 3D Boussinesq equations,” Applicable Analysis, vol. 89, no. 10, pp. 1603–1613, 2010. View at Publisher · View at Google Scholar
  11. T. Kato and G. Ponce, “Commutator estimates and the Euler and Navier-Stokes equations,” Communications on Pure and Applied Mathematics, vol. 41, no. 7, pp. 891–907, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. Y. Z. Wang, L. Hu, and Y. X. Wang, “A Beale-Kato-Madja criterion for magneto-micropolar fluid equations with partial viscosity,” Boundary Value Problems, vol. 2011, Article ID 128614, 11 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. C. Wang and Z. Zhang, “Global well-posedness for the 2-D Boussinesq system with the temperature-dependent viscosity and thermal diffusivity,” Advances in Mathematics, vol. 228, no. 1, pp. 43–62, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH