Characterization and regularity for axisymmetric solenoidal vector fields with application to navier-stokes equation


Journal Article

We consider the vorticity-stream formulation of axisymmetric incompressible flows and its equivalence with the primitive formulation. It is shown that, to characterize the regularity of a divergence free axisymmetric vector field in terms of the swirling components, an extra set of pole conditions is necessary to give a full description of the regu larity. In addition, smooth solutions up to the axis of rotation give rise to smooth solutions of primitive formulation in the case of the Navier-Stokes equation, but not the Euler equation. We also establish a proper weak formulation and show its equivalence to Leray's formulation. © 2009 Society for Industrial and Applied Mathematics.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Wang, WC

Published Date

  • December 1, 2009

Published In

Volume / Issue

  • 41 / 5

Start / End Page

  • 1825 - 1850

International Standard Serial Number (ISSN)

  • 0036-1410

Digital Object Identifier (DOI)

  • 10.1137/080739744

Citation Source

  • Scopus