Zang, Minglei; Guan, Xiaoyan Logarithmically improved regularity criteria for a fluid system with the linear Soret effect. (English) Zbl 1253.35131 Abstr. Appl. Anal. 2012, Article ID 420721, 8 p. (2012). Summary: We consider the 3D fluid system with the linear Soret effect. We obtain a logarithmically improved regularity criterion in the BMO space. MSC: 35Q35 PDEs in connection with fluid mechanics 35B65 Smoothness and regularity of solutions to PDEs Keywords:3D fluid system; linear Soret effect PDF BibTeX XML Cite \textit{M. Zang} and \textit{X. Guan}, Abstr. Appl. Anal. 2012, Article ID 420721, 8 p. (2012; Zbl 1253.35131) Full Text: DOI OpenURL References: [1] B. Straughan, The Energy Method, Stability, and Nonlinear Convection, vol. 91, Springer, New York, NY, USA, 2ND edition, 2004. · Zbl 1032.76001 [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. · Zbl 1227.76059 [4] F. Xu and J. Yuan, “Global well-posedness for a fluid system with the linear Soret effect,” submitted. · Zbl 1308.35231 [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. · Zbl 0573.76029 [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. · Zbl 0985.46015 [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. · Zbl 1171.35342 [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. · Zbl 1198.35175 [9] Y. Zhou and Z. Lei, “Logarithmically improved regularity criterion for Euler and Navier-Stokes equations,” Preprint. · Zbl 1267.35173 [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. · Zbl 1387.35501 [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. · Zbl 0671.35066 [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. · Zbl 1213.76256 [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. · Zbl 1231.35180 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.