Math @ Duke

Publications [#246944] of JianGuo Liu
Papers Published
 Liu, JG; Wang, WC, Characterization and regularity for axisymmetric solenoidal vector fields with application to navierstokes equation,
SIAM Journal on Mathematical Analysis, vol. 41 no. 5
(2009),
pp. 18251850, ISSN 00361410 [doi]
(last updated on 2017/12/13)
Abstract: We consider the vorticitystream 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 NavierStokes 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.


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