Strong solutions to the Cauchy problem of two-dimensional nonhomogeneous micropolar fluid equations with nonnegative density

2021 ◽  
Vol 18 (1) ◽  
pp. 49-69
Author(s):  
Xin Zhong
Keyword(s):  
Cauchy Problem ◽  
Micropolar Fluid ◽  
Strong Solutions ◽  
Two Dimensional ◽  
Fluid Equations ◽  
The Cauchy Problem ◽  
Micropolar Fluid Equations

Local strong solutions to the Cauchy problem of two-dimensional nonhomogeneous magneto-micropolar fluid equations with nonnegative density

2019 ◽  
pp. 1-29 ◽  
Author(s):  
Xin Zhong
Keyword(s):  
Cauchy Problem ◽  
Micropolar Fluid ◽  
Initial Density ◽  
Strong Solutions ◽  
Fluid System ◽  
The Cauchy Problem ◽  
Local Strong Solutions ◽  
Field Decay ◽  
Micropolar Fluid Equations ◽  
Local Strong Solution

We study the Cauchy problem of nonhomogeneous magneto-micropolar fluid system with zero density at infinity in the entire space [Formula: see text]. We prove that the system admits a unique local strong solution provided the initial density and the initial magnetic field decay not too slowly at infinity. In particular, there is no need to require any Choe–Kim type compatibility condition for the initial data.

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>

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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