Global smooth solutions of the generalized MHD equations with large 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 global-in-time solutions to the generalized MHD system.