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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Beale-Kato-Madja Criterion for | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 128614 14 pages doi 10.1155 2011 128614 Research Article A Beale-Kato-Madja Criterion for Magneto-Micropolar Fluid Equations with Partial Viscosity Yu-Zhu Wang 1 Liping Hu 2 and Yin-Xia Wang1 1 School of Mathematics and Information Sciences North China University of Water Resources and Electric Power Zhengzhou 450011 China 2 College of Information and Management Science Henan Agricultural University Zhengzhou 450002 China Correspondence should be addressed to Yu-Zhu Wang yuzhu108@163.com Received 18 February 2011 Accepted 7 March 2011 Academic Editor Gary Lieberman Copyright 2011 Yu-Zhu Wang 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. We study the incompressible magneto-micropolar fluid equations with partial viscosity in Wfn 2 3 . A blow-up criterion of smooth solutions is obtained. The result is analogous to the celebrated Beale-Kato-Majda type criterion for the inviscid Euler equations of incompressible fluids. 1. Introduction The incompressible magneto-micropolar fluid equations in Rn n 2 3 take the following form 1 o p 2 b 2 - xV X v 0 dtv - YAv - kV div v 2yv u -Vv - xV X u 0 1.1 dtb - vAb u Vb - b Vu 0 V u 0 V b 0 where u t x v t x b t x and p t x denote the velocity of the fluid the microrotational velocity magnetic field and hydrostatic pressure respectively. p is the kinematic viscosity X is the vortex viscosity Y and k are spin viscosities and 1 v is the magnetic Reynold. 2 Boundary Value Problems The incompressible magneto-micropolar fluid equation 1.1 has been studied extensively see 1-7 . In 2 the authors have proven that a weak solution to 1.1 has fractional time derivatives of any order less than 1 2 in the two-dimensional case. In the three-dimensional case a uniqueness result similar to the one for .
