Remarks on a Liouville-type theorem for Beltrami flows

We present a simple, short, and elementary proof that if ν is a Beltrami flow with a finite energy in ℝ³, then ν =0. In the case of the Beltrami flows satisfying ν ∈ L _loc^∞ (ℝ³) ∩ L^q(ℝ³) with q ∈ [2, 3), or |ν(x)| = O(1/|x|^1+ε) for some ε >0, we provide a different, simple proof that ν =0.