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Regularity criteria of the axisymmetric Navier-Stokes equations. (English) Zbl 0991.35063
Salvi, Rodolfo (ed.), The Navier-Stokes equations: theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, 2000. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 223, 159-165 (2002).
Summary: We present results on the regularity for axisymmetric weak solutions of the three-dimensional Navier-Stokes equations with nonzero swirl. In particular we find that the integrability of single component vorticity or velocity fields, in terms of norms with zero scaling dimension give sufficient conditions for the regularity of weak solutions. To obtain these criteria we derive new a priori estimates for the axisymmetric smooth solutions of the Navier-Stokes equations.
For the entire collection see [Zbl 0972.00046].
35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
35B45 A priori estimates in context of PDEs