scholarly journals An Omori–Yau maximum principle for semi-elliptic operators and Liouville-type theorems

2013 ◽  
Vol 31 (4) ◽  
pp. 533-539 ◽  
Author(s):  
Kyusik Hong ◽  
Chanyoung Sung
Keyword(s):  
Maximum Principle ◽  
Elliptic Operators ◽  
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.

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