Global regularity for the 3D Hall-MHD equations with low regularity axisymmetric data

TL;DR

This paper proves global regularity for 3D Hall-MHD equations with low regularity, axisymmetric initial data, and trivial swirl components, extending previous results without smallness assumptions.

Contribution

It establishes global well-posedness for the Hall-MHD system with low regularity axisymmetric data and trivial swirl, without requiring small initial data.

Findings

Global regularity proven for low regularity axisymmetric data

No smallness condition needed for initial data

Improves upon previous regularity results for Hall-MHD equations

Abstract

In this paper, we consider the global well-posedness of the incompressible Hall-MHD equations in $\mathbb{R}^3$. We prove that the solution of this system is globally regular if the initial data is axisymmetric and the swirl components of the velocity and magnetic vorticity are trivial. It should be pointed out that the initial data without any smallness and in low regularity spaces. This improves a previous result established in \cite{Fan2013}.