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 $\bu_0^ν$ with helical swirl, an analogue of the swirl component of axisymmetric flow, of magnitude $\mathcal{O}(\nu )$ in the $L^2$ norm; we assume $\bu_0^ν\to \bu_0$ in $H^1$. The new ingredient in our analysis is a decomposition of helical vector fields, through which we obtain the required estimates.

22pages

References in corpus (1)

• Global well-posedness of three-dimensional Navier-Stokes equations with partial viscosity under helical symmetry