- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 618084, 10 pages
Remarks on the Pressure Regularity Criterion of the Micropolar Fluid Equations in Multiplier Spaces
School of Science, Tianjin Polytechnic University, Tianjin 300387, China
Received 26 October 2012; Accepted 14 December 2012
Academic Editor: Beong In Yun
Copyright © 2012 Fengjun Guo. 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.
- A. C. Eringen, “Theory of micropolar fluids,” Journal of Mathematics and Mechanics, vol. 16, pp. 1–18, 1966.
- G. Böhme, Non-Newtonian Fluid Mechanics, Applied Mathematics and Mechanics, North-Holland, Amsterdam, The Netherlands, 1987.
- 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.
- B. Q. Dong and Y. Li, “Large time behavior to the system of incompressible non-Newtonian fluids in ,” Journal of Mathematical Analysis and Applications, vol. 298, no. 2, pp. 667–676, 2004.
- C. Zhao and Y. Li, “-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.
- 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.
- O. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Fluids, Gorden Brech, New York, NY, USA, 1969.
- R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, North-Holland, Amsterdam, The Netherlands, 1977.
- G. Łukaszewicz, Micropolar Fluids. Theory and Applications, Modeling and Simulation in Science, Engineering and Technology, Birkhäauser, Boston, Mass, USA, 1999.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- P. G. Lemarié-Rieusset, Recent Developments in the Navier-Stokes Problem, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2002.
- Y. Zhou, “On regularity criteria in terms of pressure for the Navier-Stokes equations in ,” Proceedings of the American Mathematical Society, vol. 134, no. 1, pp. 149–156, 2006.
- Y. Zhou, “On a regularity criterion in terms of the gradient of pressure for the Navier-Stokes equations in ,” Zeitschrift für Angewandte Mathematik und Physik, vol. 57, no. 3, pp. 384–392, 2006.