Publications [#246944] of Jian-Guo Liu

Papers Published

  1. Liu, JG; Wang, WC, Characterization and regularity for axisymmetric solenoidal vector fields with application to navier-stokes equation, Siam Journal on Mathematical Analysis, vol. 41 no. 5 (December, 2009), pp. 1825-1850, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
    (last updated on 2019/07/22)

    Abstract:
    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.