Global smooth solutions of the 3D Hall-magnetohydrodynamic equations with large data

TL;DR

This paper proves the existence of global smooth solutions for the 3D Hall-MHD equations with large initial data, using a novel splitting method to handle large initial norms.

Contribution

It introduces a new approach to establish global solutions for large initial data in 3D Hall-MHD equations, expanding the understanding of their long-term behavior.

Findings

Global existence for large initial data established

Constructed examples of large initial conditions

Method involves splitting heat equations to control solutions

Abstract

In this paper, we establish the global existence to the three-dimensional incompressible Hall-MHD equations for a class of large initial data, whose $L^{\infty}$ norms can be arbitrarily large. In addition , we give an example to show that such a large initial value does exist. Our idea is splitting the generalized heat equations from Hall-MHD system to generate a small quantity for large time $t$.