Axially symmetric flows of ideal and viscous fluids filling the whole space: PMM vol. 32, no. 1, 1968, pp. 59–69

Abstract

In this work, we investigate the axisymmetric MHD system with nearly critical initial data having the special structure: u0=u0rer+u0θeθ+u0zez,b0=b0θeθ. It is proved that if the scaling-invariant norm ‖ru0θ‖L∞ is sufficiently small, then this system is globally well-posed.