Blow-up criterion for 3D viscous-resistive compressible magnetohydrodynamic equations

2012 ◽  
Vol 36 (9) ◽  
pp. 1145-1156 ◽  
Author(s):  
Mingtao Chen ◽  
Shengquan Liu
Keyword(s):  
Blow Up ◽  
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.

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