Remarks on Leray's self‐similar solutions to the 3D magnetohydrodynamic equations

In this note, we examine small self-similar solutions of the 3D incompressible magnetohydrodynamic equations in homogenous function spaces and show the uniqueness of self-similar solutions when the velocity field is small in some homogeneous function spaces. This extend the recent results given by C. He and Z. Xin. On the self-similar solutions of the magneto-hydro-dynamic equations. Acta Mathematica Scientia, serie B English Edition 2009; 29 (3): 583-598. It is a natural way to extend the space widely and improve the previous results. Copyright (c) 2013 John Wiley & Sons, Ltd.