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 $t$.

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• A class of global large, smooth solutions for the magnetohydrodynamics with the Hall and ion-slip effects