Global Smooth Solutions of the Generalized MHD Equations with Large Initial Data

Abstract

In this paper, we consider the Cauchy problem of the multi-dimensional generalized MHD system in the whole space and construct global smooth solutions with a class of large initial data by exploring the structure of the nonlinear term. Precisely speaking, our choice of special initial data whose $$L^{\infty }$$ norm can be arbitrarily large allows to generate a unique global-in-time solution to the generalized MHD system.