scholarly journals Logarithmically Improved Regularity Criterion for the 3D Micropolar Fluid Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Zhang
Keyword(s):  
Besov Space ◽  
Strong Solution ◽  
Weak Solutions ◽  
Micropolar Fluid ◽  
Regularity Criterion ◽  
Vorticity Field ◽  
Regularity Of Weak Solutions ◽  
Fluid Equations ◽  
Incompressible Micropolar Fluid ◽  
Micropolar Fluid Equations

We study the regularity of weak solutions to the incompressible micropolar fluid equations. We obtain an improved regularity criterion in terms of vorticity of velocity in Besov space. It is proved that if the vorticity field satisfies ∫0T∇×uB˙∞,∞0/1+log1+∇×uB˙∞,∞0dt<∞ then the strong solution can be smoothly extended after time T.

scholarly journals A Regularity Criterion for the Magneto-Micropolar Fluid Equations inB˙∞,∞−1

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhihao Tang ◽  
Gang Wang ◽  
Haiwa Guan
Keyword(s):  
Cauchy Problem ◽  
Besov Space ◽  
Micropolar Fluid ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Fluid Equations ◽  
The Cauchy Problem ◽  
Homogeneous Besov Space ◽  
Micropolar Fluid Equations

The paper is dedicated to study of the Cauchy problem for the magneto-micropolar fluid equations in three-dimensional spaces. A new logarithmically improved regularity criterion for the magneto-micropolar fluid equations is established in terms of the pressure in the homogeneous Besov spaceB˙∞,∞−1.

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