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

Author(s)

Jiu, Quansen ; Lopes Filho, Milton C. ; Niu, Dongjuan ; Nussenzveig Lopes, Helena J.

• Document type: Journal article
• Source: PHYSICA D-NONLINEAR PHENOMENA; v. 376, p. 9-pg., 2018-08-01.

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)(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. (AU)

• FAPESP's process: 08/09473-0 - Boundary layers in incompressible flows
• Grantee: Dongjuan Niu
• Support Opportunities: Scholarships in Brazil - Post-Doctoral