Blow-up criteria of strong solutions to the 3D micropolar fluid equations with partial viscosities

2021 ◽  
Vol 51 (1) ◽  
Author(s):  
Hui Zhang
Keyword(s):  
Micropolar Fluid ◽  
Blow Up ◽  
Strong Solutions ◽  
Fluid Equations ◽  
Micropolar Fluid Equations

scholarly journals Logarithmically Improved Blow up Criterion for Smooths Solution to the 3D Micropolar Fluid Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yin-Xia Wang ◽  
Hengjun Zhao
Keyword(s):  
Micropolar Fluid ◽  
Blow Up ◽  
Smooth Solutions ◽  
Fluid Equations ◽  
Micropolar Fluid Equations ◽  
Blow Up Criterion

Blow-up criteria of smooth solutions for the 3D micropolar fluid equations are investigated. Logarithmically improved blow-up criteria are established in the Morrey-Campanto space.

scholarly journals Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xin Zhong
Keyword(s):  
Exponential Decay ◽  
Micropolar Fluid ◽  
Rotational Velocity ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Slip Boundary Condition ◽  
Dirichlet Boundary Conditions ◽  
Fluid Equations ◽  
Micropolar Fluid Equations

<p style='text-indent:20px;'>We consider an initial boundary value problem of three-dimensional (3D) nonhomogeneous magneto-micropolar fluid equations in a bounded simply connected smooth domain with homogeneous Dirichlet boundary conditions for the velocity and micro-rotational velocity and Navier-slip boundary condition for the magnetic field. We prove the global existence and exponential decay of strong solutions provided that some smallness condition holds true. Note that although the system degenerates near vacuum, there is no need to require compatibility conditions for the initial data via time weighted techniques.</p>

scholarly journals Global strong solution to the nonhomogeneous micropolar fluid equations with large initial data and vacuum

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xin Zhong
Keyword(s):  
Initial Data ◽  
Micropolar Fluid ◽  
Structural Characteristics ◽  
Initial Density ◽  
Strong Solutions ◽  
Energy Estimates ◽  
Global Strong Solution ◽  
Fluid Equations ◽  
The Cauchy Problem ◽  
Micropolar Fluid Equations

<p style='text-indent:20px;'>We study the Cauchy problem of nonhomogeneous micropolar fluid equations with zero density at infinity in the whole plane <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula>. We derive the global existence and uniqueness of strong solutions if the initial density decays not too slowly at infinity. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Our method relies upon the delicate weighted energy estimates and the structural characteristics of the system under consideration.</p>

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