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

TL;DR

This paper proves the global existence of smooth solutions for 3D non-resistive MHD equations with low regularity, axisymmetric initial data lacking swirl, expanding understanding of solution behavior under minimal regularity conditions.

Contribution

It establishes the global well-posedness of classical solutions for 3D non-resistive MHD equations with low regularity axisymmetric data and no swirl, a significant extension in the field.

Findings

Global well-posedness for low regularity initial data

Solutions can be arbitrarily large in size

Applicable to axisymmetric flows without swirl

Abstract

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 classical solutions if the initial data is axially symmetric and the swirl components of the velocity and magnetic vorticity vanish. In particular, the special axially symmetric initial data can be arbitrarily large and satisfy low regularity assumptions.