Global well-posedness of the 3D Navier-Stokes equations with helical $L^1$ vorticity

We show that the Navier-Stokes equations on $\mathbb R^2\times\mathbb T$ are globally well posed for initial vorticities that are both helically symmetric and integrable. This class of data typically generates velocity fields of infinite kinetic energy, so this result is not covered by the classical