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arXiv · 1706.10012

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

Quansen Jiu·Milton C. Lopes Filho·Dongjuan Niu·Helena J. Nussenzveig Lopes
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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 $\bu_0^\nu$ with helical swirl, an analogue of the swirl component of axisymmetric flow, of magnitude $\mathcal{O}(\nu)$ in the $L^2$ norm; we assume $\bu_0^\nu \to \bu_0$ in $H^1$. The new ingredient in our analysis is a decomposition of helical vector fields, through which we obtain the required estimates.

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Quansen Jiu, Milton C. Lopes Filho, Dongjuan Niu, Helena J. Nussenzveig Lopes. 2017-06-30. The limit of vanishing viscosity for the incompressible 3D Navier-Stokes equations with helical symmetry. https://doi.org/10.1016/j.physd.2018.01.013

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