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 ∈ L ∞ loc ( R 3 ) ∩ L q ( R 3 ) with q ∈ [2 , 3 ) ,or | v( x ) |= O ( 1 / | x | 1 + ε ) for some ε> 0, we provide a different, simple proof that v = 0.