scholarly journals A blow-up criterion for three-dimensional compressible magnetohydrodynamic equations with variable viscosity

2019 ◽  
Vol 24 (7) ◽  
pp. 3249-3264
Author(s):  
Xin Zhong ◽  
Keyword(s):  
Blow Up ◽  
Variable Viscosity ◽  
Three Dimensional ◽  
Magnetohydrodynamic Equations ◽  
Blow Up Criterion

A BLOW-UP CRITERION FOR 3D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM

2012 ◽  
Vol 22 (02) ◽  
pp. 1150010 ◽  
Author(s):  
XINYING XU ◽  
JIANWEN ZHANG
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Magnetohydrodynamic Equations ◽  
The Cauchy Problem ◽  
Blow Up Criterion

This paper is concerned with a blow-up criterion of strong solutions for three-dimensional compressible isentropic magnetohydrodynamic equations with vacuum. It is shown that if the density and velocity satisfy [Formula: see text], where [Formula: see text], 3 < r ≤ ∞ and [Formula: see text] denotes the weak Lr-space, then the strong solutions to the Cauchy problem of the compressible magnetohydrodynamic equations can exist globally over [0, T].

A LOGARITHMALLY IMPROVED BLOW-UP CRITERION OF SMOOTH SOLUTIONS FOR THE THREE-DIMENSIONAL MHD EQUATIONS

2012 ◽  
Vol 23 (02) ◽  
pp. 1250027 ◽  
Author(s):  
YU-ZHU WANG ◽  
HENGJUN ZHAO ◽  
YIN-XIA WANG
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Magnetohydrodynamic Equations ◽  
Smooth Solutions ◽  
The Cauchy Problem ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Blow Up Criterion

In this paper we investigate the Cauchy problem for the three-dimensional incompressible magnetohydrodynamic equations. A logarithmal improved blow-up criterion of smooth solutions is obtained.

scholarly journals Blow-Up Criterion of Weak Solutions for the 3D Boussinesq Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Zhaohui Dai ◽  
Xiaosong Wang ◽  
Lingrui Zhang ◽  
Wei Hou
Keyword(s):  
Weak Solutions ◽  
Blow Up ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Interpolation Inequality ◽  
Embedding Theorem ◽  
The Earth ◽  
The Cauchy Problem ◽  
Homogeneous Besov Space ◽  
Blow Up Criterion

The Boussinesq equations describe the three-dimensional incompressible fluid moving under the gravity and the earth rotation which come from atmospheric or oceanographic turbulence where rotation and stratification play an important role. In this paper, we investigate the Cauchy problem of the three-dimensional incompressible Boussinesq equations. By commutator estimate, some interpolation inequality, and embedding theorem, we establish a blow-up criterion of weak solutions in terms of the pressurepin the homogeneous Besov spaceḂ∞,∞0.

Local existence and Serrin-type blow-up criterion for strong solutions to the radiation hydrodynamic equations

2020 ◽  
Vol 17 (03) ◽  
pp. 501-557
Author(s):  
Hao Li ◽  
Yachun Li
Keyword(s):  
Blow Up ◽  
Initial Density ◽  
Local Existence ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Hydrodynamic Equations ◽  
Open Set ◽  
The Cauchy Problem ◽  
Local Strong Solutions ◽  
Blow Up Criterion

We consider the Cauchy problem for the three-dimensional, compressible radiation hydrodynamic equations. We establish the existence and uniqueness of local strong solutions for large initial data satisfying some compatibility condition. The initial density need not be positive and may vanish in an open set. Moreover, we establish a Serrin-type blow-up criterion, which is stated in terms of the velocity and density variables [Formula: see text] and is independent of the temperature and the radiation intensity.

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