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

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 $t$.