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arXiv · 1903.03212

Global Large Smooth Solutions for 3-D Hall-magnetohydrodynamics

Huali Zhang
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Abstract

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 from the second-order semi-linear equations to the second-order quasilinear equations, because the Hall term elevates the Hall-MHD system to the quasilinear level.

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Huali Zhang. 2019-03-07. Global Large Smooth Solutions for 3-D Hall-magnetohydrodynamics. https://arxiv.org/abs/1903.03212

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