Communications in Mathematical Sciences

Volume 20 (2022)

Number 7

Global smooth solutions to the 3D non-resistive MHD equations with low regularity axisymmetric data

Pages: 1979 – 1994



Xiaolian Ai (School of Mathematics, Northwest University, Xi’an, China)

Zhouyu Li (School of Sciences, Xi’an University of Technology, Xi’an, China)


The purpose of this paper is to study the incompressible non-resistive MHD equations in $\mathbb{R}^3$. We establish the global well-posedness of the system if the initial data is axially symmetric and the swirl component of the velocity and the magnetic vorticity vanish. In particular, the special axially symmetric initial data can be arbitrarily large and satisfy low regularity assumptions.


non-resistive MHD equations, axisymmetric solutions, global regularity

2010 Mathematics Subject Classification

35Q35, 76D03

The work is partially supported by the National Natural Science Foundation of China under the grants 11571279, 11601423 and 11931013.

Received 14 February 2021

Received revised 11 November 2021

Accepted 6 February 2022

Published 21 October 2022