Liouville Type Theorem for the Stationary Equations of Magneto-Hydrodynamics

Abstract

We show that any smooth solution (u, H) to the stationary equations of magneto-hydrodynamics 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 integra-bility and the additional assumption ∇u,∇H ∈ L2(ℝ3), i.e., finite Dirichlet integral.