On local strong solutions to the Cauchy problem of the two-dimensional full compressible magnetohydrodynamic equations with vacuum and zero heat conduction

2016 ◽  
Vol 31 ◽  
pp. 409-430 ◽  
Author(s):  
Li Lu ◽  
Bin Huang
Keyword(s):  
Cauchy Problem ◽  
Heat Conduction ◽  
Strong Solutions ◽  
Two Dimensional ◽  
Magnetohydrodynamic Equations ◽  
The Cauchy Problem ◽  
Local Strong Solutions

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].

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.

Sign in / Sign up

Export Citation Format

Share Document