The inviscid limit of the incompressible 3D Navier–Stokes equations with helical symmetry

5 years ago

The inviscid limit of 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

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} \to 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.

Publisher URL: www.sciencedirect.com/science

DOI: S0167278917303445

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