REMARKS ON THE LIOUVILLE TYPE THEOREMS FOR THE 3D STATIONARY MHD EQUATIONS

In this paper we study the stationary incompressible MHD equations on R-3. We show that the velocity field u and the magnetic field b, which vanish at infinity, must be identically zero, provided that del u and del b belong to L-q(R-3) for some q is an element of(3/2 , 2], and u belongs to BMO-1(R-3). Moreover, motivated by the recent work [19], we also obtain the Liouville type theorem by assuming that (u, b) is axisymmetric and u satisfies some decay property.