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 Global well-posedness and optimal time decay rates of solutions to the three-dimensional magneto-micropolar fluid equations

2021 ◽  
Author(s):  
Dongjuan Niu ◽  
Haifeng Shang
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Besov Spaces ◽  
Micropolar Fluid ◽  
Three Dimensional ◽  
Decay Rates ◽  
Decay Estimates ◽  
Optimal Decay ◽  
Fluid Equations ◽  
Micropolar Fluid Equations

This paper deals with the global existence and decay estimates of solutions to the three-dimensional magneto-micropolar fluid equations with only velocity dissipation and magnetic diffusion in the whole space with various Sobolev and Besov spaces. Specifically, we first investigate the global existence and optimal decay estimates of weak solutions. Then we prove the global existence of solutions with small initial data in $H^s$, $B_{2, \infty}^s$ and critical Besov spaces, respectively. Furthermore, the optimal decay rates of these global solutions are correspondingly established in $\dot{H}^m$ and $\dot{B}_{2, \infty}^m$ spaces with $0\leq m\leq s$ and in $\dot{B}_{2, 1}^{m}$ with $0\leq m\leq \frac 12$, when the initial data belongs to $\dot{B}_{2, \infty}^{-l}$ ($0< l\leq\frac32$). The main difficulties lie in the presence of linear terms and the lack of micro-rotation velocity dissipation. To overcome them, we make full use of the special structure of the system and employ various techniques involved with the energy methods, the improved Fourier splitting, Fourier analysis and the regularity interpolation methods.

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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