A Priori Bounds for the Vorticity of Axis Symmetric Solutions to the Navier-Stokes Equations

Abstract

We obtain a pointwise, a priori bound for the vorticity of axis symmetric solutions to the 3 dimensional Navier-Stokes equations. The bound is in the form of a reciprocal of a power of the distance to the axis of symmetry. This seems to be the first general pointwise estimate established for the axis symmetric Navier-Stokes equations.

one reference added; some notations changed and typos cleared following suggestions by Prof. T.P. Tsai

References in corpus (3)

• Dynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl
• Liouville theorems for the Navier-Stokes equations and applications
• On Type I singularities of the local axi-symmetric solutions of the Navier-Stokes equations