scholarly journals Remarks on Liouville-Type Theorems for the Steady MHD and Hall-MHD Equations

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Xiaomeng Chen ◽  
Shuai Li ◽  
Wendong Wang
Keyword(s):  
Mhd Equations ◽  
Liouville Type ◽  
Liouville Type Theorems ◽  
Hall Mhd

scholarly journals Liouville-type theorems for the stationary MHD equations in 2D

Nonlinearity ◽  
2019 ◽  
Vol 32 (11) ◽  
pp. 4483-4505 ◽  
Author(s):  
Wendong Wang ◽  
Yuzhao Wang
Keyword(s):  
Mhd Equations ◽  
Liouville Type ◽  
Liouville Type Theorems

scholarly journals On Liouville-type theorems for the 2D stationary MHD equations

Nonlinearity ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 870-888
Author(s):  
Nicola De Nitti ◽  
Francis Hounkpe ◽  
Simon Schulz
Keyword(s):  
Magnetic Field ◽  
Maximum Principle ◽  
Diffusion Equation ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Drift Diffusion ◽  
Liouville Type ◽  
Dirichlet Integral ◽  
Liouville Type Theorems ◽  
The Magnetic Field

Abstract We establish new Liouville-type theorems for the two-dimensional stationary magneto-hydrodynamic incompressible system assuming that the velocity and magnetic field have bounded Dirichlet integral. The key tool in our proof is observing that the stream function associated to the magnetic field satisfies a simple drift–diffusion equation for which a maximum principle is available.

scholarly journals Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

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