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

PHYSICA D-NONLINEAR PHENOMENA

卷:376

Article

Jiu, Quansen¹  Lopes Filho, Milton C.²  Niu, Dongjuan¹  Nussenzveig Lopes, Helena J.² 

[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

[2] Univ Fed Rio de Janeiro, Inst Matemat, Caixa Postal 68530, BR-21941909 Rio De Janeiro, RJ, Brazil

关键词: Navier-Stokes equations;    Euler equations;    Helical symmetry;    Vanishing viscosity limit;   

DOI  :  10.1016/j.physd.2018.01.013

来源: Elsevier

【 摘 要 】

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)(v) with helical swirl, an analogue of the swirl component of axisymmetric flow, of magnitude O(v) in the L-2 norm; we assume u(0)(v) -> 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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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