Global smooth solutions of MHD equations with large data

TL;DR

This paper proves the existence of smooth solutions for the 3D MHD equations with large initial data, showing that solutions can exist globally even when initial velocity and magnetic fields are arbitrarily large.

Contribution

It establishes the first known global existence of smooth solutions for large initial data in the 3D MHD system.

Findings

Global smooth solutions exist for large initial data.

Initial velocity and magnetic field can be arbitrarily large in the critical norm.

The results extend the understanding of the MHD system's well-posedness.

Abstract

In this paper, we establish the global existence of smooth solutions of the three-dimensional MHD system for a class of large initial data. Both the initial velocity and magnetic field can be arbitrarily large in the critical norm.