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In this paper, the global smooth solution of Cauchy's problem ofincompressible, resistive, viscous Hall-magnetohydrodynamics (Hall-MHD) isstudied. By exploring the nonlinear structure of Hall-MHD equations, a class oflarge initial data is constructed, which can be arbitrarily large in$H^3(\mathbb{R}^3)$. Our result may also be considered as the extension of workof Lei-Lin-Zhou from the second-order semi-linear equations to the second-orderquasilinear equations, because the Hall term elevates the Hall-MHD system tothe quasilinear level.

Global Large Smooth Solutions for 3-D Hall-magnetohydrodynamics