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

Abstract 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 u 0 ν with helical swirl, an analogue of the swirl component of axisymmetric flow, of magnitude O ( ν ) in the L 2 norm; we assume u 0 ν → u 0 in H 1 . The new ingredient in our analysis is a decomposition of helical vector fields, through which we obtain the required estimates.