Liouville type theorem for double Beltrami solutions of the Hall-MHD system in R³

In this paper we prove Liouville type theorem for the double Beltrami solutions to the stationary Hall-MHD equations in R³. Let $(u, B)$ be a smooth double Beltrami solution to the stationary Hall-MHD equations in R³, satisfying ∫R³ (|u|q + |B|q )dx <+∞ for some q∈ [2, 3), then $u=B=0$. In the case of $B=0$ the theorem reduces the previously known Liouville type result for the Beltrami solutions to the Euler equations.