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Linked References

1. A. C. Eringen, “Theory of micropolar fluids,” Journal of Mathematics and Mechanics, vol. 16, pp. 1–18, 1966. View at MathSciNet
2. G. Böhme, Non-Newtonian Fluid Mechanics, Applied Mathematics and Mechanics, North-Holland, Amsterdam, The Netherlands, 1987. View at MathSciNet
3. J. Málek, J. Nečas, M. Rokyta, and M. Ružička, Weak and Measure-valued Solutions to Evolutionary PDEs, vol. 13, Chapman & Hall, New York, NY, USA, 1996. View at MathSciNet
4. B. Q. Dong and Y. Li, “Large time behavior to the system of incompressible non-Newtonian fluids in ${ℝ}^2$,” Journal of Mathematical Analysis and Applications, vol. 298, no. 2, pp. 667–676, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
5. C. Zhao and Y. Li, “$H^2$-compact attractor for a non-Newtonian system in two-dimensional unbounded domains,” Nonlinear Analysis: Theory, Methods & Applications, vol. 56, no. 7, pp. 1091–1103, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
6. C. Zhao and S. Zhou, “Pullback attractors for a non-autonomous incompressible non-Newtonian fluid,” Journal of Differential Equations, vol. 238, no. 2, pp. 394–425, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
7. O. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Fluids, Gorden Brech, New York, NY, USA, 1969.
8. R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, North-Holland, Amsterdam, The Netherlands, 1977. View at MathSciNet
9. G. Łukaszewicz, Micropolar Fluids. Theory and Applications, Modeling and Simulation in Science, Engineering and Technology, Birkhäauser, Boston, Mass, USA, 1999. View at MathSciNet
10. B.-Q. Dong and Z. Zhang, “Global regularity of the 2D micropolar fluid flows with zero angular viscosity,” Journal of Differential Equations, vol. 249, no. 1, pp. 200–213, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
11. N. Yamaguchi, “Existence of global strong solution to the micropolar fluid system in a bounded domain,” Mathematical Methods in the Applied Sciences, vol. 28, no. 13, pp. 1507–1526, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
12. B.-Q. Dong and Z.-M. Chen, “Global attractors of two-dimensional micropolar fluid flows in some unbounded domains,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 610–620, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
13. B.-Q. Dong and Z.-M. Chen, “On upper and lower bounds of higher order derivatives for solutions to the 2D micropolar fluid equations,” Journal of Mathematical Analysis and Applications, vol. 334, no. 2, pp. 1386–1399, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
14. G. P. Galdi and S. Rionero, “A note on the existence and uniqueness of solutions of the micropolar fluid equations,” International Journal of Engineering Science, vol. 15, no. 2, pp. 105–108, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
15. B.-Q. Dong and Z.-M. Chen, “Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows,” Discrete and Continuous Dynamical Systems A, vol. 23, no. 3, pp. 765–784, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
16. B.-Q. Dong and Z.-M. Chen, “Regularity criteria of weak solutions to the three-dimensional micropolar flows,” Journal of Mathematical Physics, vol. 50, no. 10, article 103525, 13 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
17. B.-Q. Dong and W. Zhang, “On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 73, no. 7, pp. 2334–2341, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
18. B. Yuan, “On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space,” Proceedings of the American Mathematical Society, vol. 138, no. 6, pp. 2025–2036, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
19. B.-Q. Dong, Y. Jia, and Z.-M. Chen, “Pressure regularity criteria of the three-dimensional micropolar fluid flows,” Mathematical Methods in the Applied Sciences, vol. 34, no. 5, pp. 595–606, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
20. Y. Jia, W. Zhang, and B.-Q. Dong, “Remarks on the regularity criterion of the 3D micropolar fluid flows in terms of the pressure,” Applied Mathematics Letters, vol. 24, no. 2, pp. 199–203, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
21. Q. Chen, C. Miao, and Z. Zhang, “On the regularity criterion of weak solution for the 3D viscous magneto-hydrodynamics equations,” Communications in Mathematical Physics, vol. 284, no. 3, pp. 919–930, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
22. B.-Q. Dong, Y. Jia, and W. Zhang, “An improved regularity criterion of three-dimensional magnetohydrodynamic equations,” Nonlinear Analysis: Real World Applications, vol. 13, no. 3, pp. 1159–1169, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
23. C. He and Z. Xin, “On the regularity of weak solutions to the magnetohydrodynamic equations,” Journal of Differential Equations, vol. 213, no. 2, pp. 235–254, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
24. B.-Q. Dong and Z. Zhang, “The BKM criterion for the 3D Navier-Stokes equations via two velocity components,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 2415–2421, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
25. C. Cao and J. Wu, “Two regularity criteria for the 3D MHD equations,” Journal of Differential Equations, vol. 248, no. 9, pp. 2263–2274, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
26. Y. Zhou, “A new regularity criterion for weak solutions to the Navier-Stokes equations,” Journal de Mathématiques Pures et Appliquées, vol. 84, no. 11, pp. 1496–1514, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
27. B. Dong, G. Sadek, and Z. Chen, “On the regularity criteria of the 3D Navier-Stokes equations in critical spaces,” Acta Mathematica Scientia B, vol. 31, no. 2, pp. 591–600, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
28. P. G. Lemarié-Rieusset, Recent Developments in the Navier-Stokes Problem, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
29. Y. Zhou, “On regularity criteria in terms of pressure for the Navier-Stokes equations in ${ℝ}^3$,” Proceedings of the American Mathematical Society, vol. 134, no. 1, pp. 149–156, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
30. Y. Zhou, “On a regularity criterion in terms of the gradient of pressure for the Navier-Stokes equations in ${ℝ}^n$,” Zeitschrift für Angewandte Mathematik und Physik, vol. 57, no. 3, pp. 384–392, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet