We prove refined Liouville-type theorems for smooth solutions to the three-dimensional stationary MHD equations. Under a mild growth condition involving a function g (ρ) (monotone, \ (^-1 / 3 g () 0, \) and \ (. ^ d g () =) \), any solution with velocity and magnetic field growing at most like \ (^2{p-13} g () ^3{p-1}\) for some 3/2 < p < 3 must be identically zero. This extends recent sharp Liouville theorems for the Navier-Stokes equations to the MHD case and allows for logarithmic or even weaker subcritical growth.
Xiangyi Zhang (Mon,) studied this question.