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