On Liouville type theorems for the stationary MHD and Hall-MHD systems

A note on the Liouville type theorem for the smooth solutions of the stationary Hall-MHD system

On the von Kármán-Howarth equations for Hall MHD flows

The von Kármán-Howarth equations are derived for three-dimensional (3D) Hall magnetohydrodynamics (MHD) in the case of an homogeneous and isotropic turbulence. From these equations, we derive exact scaling laws for the third-order correlation tensors. We show how these relations are compatible with previous heuristic and numerical results. These multi-scale laws provide a relevant tool to inves...

Liouville-Type Theorems for Some Integral Systems

/2 ( ) ( ) u u        where  is the Fourier transformation and  its inverse. The question is to determine for which values of the exponents pi and qi the only nonnegative solution (u, v) of (1) and (2) is trivial, i.e., (u; v) = (0, 0). When 2   , is the case of the Emden-Fowler equation 0 , 0     u u u k in N  (5) When ) 3 )( 2 /( ) 2 ( 1      N N N k , it has been prove...

A Two-level Discretization Method for the Stationary Mhd Equations∗

We describe and analyze a two-level finite-element method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics (or MHD). These equations, which model the flow of electrically conducting fluids in the presence of electromagnetic fields, arise in plasma physics and liquid-metal technology as well as in geophysics and astronomy. We treat the equations under ph...

Hall Effects on MHD Couette Flow in Rotating System

Hall effects on the MHD Couette flow between two infinite horizontal parallel porous plates in a rotating system under the boundary layer approximations have been studied. One of the plate is held at rest and the other one moves with uniform velocity. An exact solution of governing equation has obtained in closed form. Asymptotic behavior of the solution has analyzed for large values of magneti...