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November  2019, 39(11): 6669-6682. doi: 10.3934/dcds.2019290

## Global large smooth solutions for 3-D Hall-magnetohydrodynamics

 Changsha University of Science and Technology, School of Mathematics and Statistics, Changsha 410114, China

* Corresponding author: Huali Zhang

Received  March 2019 Published  August 2019

Fund Project: The first author is supported by Education Department of Hunan Province, general Program(grant No.17C0039), and Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on Transportation, Changsha University of Science and Technology, Changsha; 410114, China.

In this paper, the global smooth solution of Cauchy's problem of incompressible, resistive, viscous Hall-magnetohydrodynamics (Hall-MHD) is studied. By exploring the nonlinear structure of Hall-MHD equations, a class of large 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 work of Lei-Lin-Zhou [15] from the second-order semilinear equations to the second-order quasilinear equations, because the Hall term elevates the Hall-MHD system to the quasilinear level.

Citation: Huali Zhang. Global large smooth solutions for 3-D Hall-magnetohydrodynamics. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6669-6682. doi: 10.3934/dcds.2019290
##### References:

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