Remarks on a Liouville-Type Theorem for Beltrami Flows

Abstract

We present a simple, short, and elementary proof that if v is a Beltrami flow with a finite energy in R-3, then v = 0. In the case of the Beltrami flows satisfying v is an element of L-loc(infinity)(R-3) boolean AND L-q(R-3) with q is an element of[2, 3), or vertical bar v(x)vertical bar = O(1/vertical bar x vertical bar(1+epsilon)) for some epsilon > 0, we provide a different, simple proof that v = 0.