The Liouville Property and Regularity of Weak Beltrami Flows

Abstract

We will look at Beltrami flows with respect to weak solutions in the case of stationary Euler equations in R3. Given this weak Beltrami flow, we will look at showing the regulariry and Liouville property. We will show that given a specific decay property of the tangential portion of the velocity at infinity, then the solution is trivial. In doing so, we will show other relatations for the tangential and normal components of the weak solutions to the stationary Euler equations.