scholarly journals A regularity criterion for the three-dimensional micropolar fluid system in homogeneous Besov spaces

2016 ◽  
pp. 1-6 ◽  
Author(s):  
Zujin Zhang
Keyword(s):  
Besov Spaces ◽  
Micropolar Fluid ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Fluid System

scholarly journals Logarithmical Regularity Criteria of the Three-Dimensional Micropolar Fluid Equations in terms of the Pressure

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yan Jia ◽  
Jing Zhang ◽  
Bo-Qing Dong
Keyword(s):  
Partial Derivative ◽  
Besov Spaces ◽  
Micropolar Fluid ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Regularity Criteria ◽  
Lebesgue Spaces ◽  
Fluid Equations ◽  
Micropolar Fluid Equations

This paper is devoted to the regularity criterion of the three-dimensional micropolar fluid equations. Some new regularity criteria in terms of the partial derivative of the pressure in the Lebesgue spaces and the Besov spaces are obtained which improve the previous results on the micropolar fluid equations.

scholarly journals A new blow up criterion for the 3D magneto-micropolar fluid flows without magnetic diffusion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Dongxiang Chen ◽  
Qifeng Liu
Keyword(s):  
Magnetic Field ◽  
Weak Solution ◽  
Micropolar Fluid ◽  
Blow Up ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Regularity Criterion ◽  
Gradient Field ◽  
Magnetic Diffusion ◽  
The Magnetic Field

AbstractThis note obtains a new regularity criterion for the three-dimensional magneto-micropolar fluid flows in terms of one velocity component and the gradient field of the magnetic field. The authors prove that the weak solution $(u,\omega,b)$ ( u , ω , b ) to the magneto-micropolar fluid flows can be extended beyond time $t=T$ t = T , provided if $u_{3}\in L^{\beta }(0,T;L^{\alpha }(R^{3}))$ u 3 ∈ L β ( 0 , T ; L α ( R 3 ) ) with $\frac{2}{\beta }+\frac{3}{\alpha }\leq \frac{3}{4}+\frac{1}{2\alpha },\alpha > \frac{10}{3}$ 2 β + 3 α ≤ 3 4 + 1 2 α , α > 10 3 and $\nabla b\in L^{\frac{4p}{3(p-2)}}(0,T;\dot{M}_{p,q}(R^{3}))$ ∇ b ∈ L 4 p 3 ( p − 2 ) ( 0 , T ; M ˙ p , q ( R 3 ) ) with $1< q\leq p<\infty $ 1 < q ≤ p < ∞ and $p\geq 3$ p ≥ 3 .

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