Global large smooth solutions for 3-D Hall-magnetohydrodynamics

Huali Zhang

doi:10.3934/dcds.2019290

Article Contents

2019, Volume 39, Issue 11: 6669-6682. Doi: 10.3934/dcds.2019290

This issue Previous Article Scattering of radial data in the focusing NLS and generalized Hartree equations Next Article Electro-magneto-static study of the nonlinear Schrödinger equation coupled with Bopp-Podolsky electrodynamics in the Proca setting

Global large smooth solutions for 3-D Hall-magnetohydrodynamics

Huali Zhang^,

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

^* Corresponding author: Huali Zhang
^* Corresponding author: Huali Zhang

Received: February 28, 2019

Published: August 2019

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

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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.

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Mathematics Subject Classification: Primary: 35A01, 35A02, 35A09; Secondary: 35E15, 35Q35.

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