Abstract: We show that any smooth solution (u, H) to the stationary equations of magnetohydrodynamics belonging to both spaces L⁶(R³) and BMO^-1(R³) must be identically zero. This is an extension of previous results, all of which systematically required stronger integrability and the additional assumption ▽u, ▽H ∈ L²(R³), i.e., finite Dirichlet integral.

Key words: Liouville theorem, Caccioppoli inequality, Navier-Stokes equations, MHD