- Published 2009 in SIAM J. Math. Analysis

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 condition is necessary to give a full description of the regularity. In addition, smooth solutions up to the axis of rotation gives rise to smooth solutions of primitive formulation in the case of Navier-Stokes equations, but not the Euler equations. We also establish proper weak formulations and show its equivalence to Leray’s solutions.

@article{Liu2009CharacterizationAR,
title={Characterization and Regularity for Axisymmetric Solenoidal Vector Fields with Application to Navier-Stokes Equation},
author={Jian-Guo Liu and Wei-Cheng Wang},
journal={SIAM J. Math. Analysis},
year={2009},
volume={41},
pages={1825-1850}
}