The limit of vanishing viscosity for the incompressible 3D Navier-Stokes equations with helical symmetry

In this paper, we are concerned with the vanishing viscosity problem for the three-dimensional Navier-Stokes equations with helical symmetry, in the whole space. We choose viscosity-dependent initial u0ν with helical swirl, an analogue of the swirl component of axisymmetric flow, of magnitude O(ν) in the L2 norm; we assume u0ν→u0 in H1. The new ingredient in our analysis is a decomposition of helical vector fields, through which we obtain the required estimates.