Global Existence and Uniqueness of Weak Solutions of 3-D Euler Equations with Helical Symmetry in the Absence of Vorticity Stretching

Abstract

We prove uniqueness and existence of the weak solutions of Euler equations with helical symmetry, with initial vorticity in $L^{\infty}$ under "no vorticity stretching" geometric constraint. Our article follows the argument of the seminal work of Yudovich. We adjust the argument to resolve the difficulties which are specific to the helical symmetry.