Global solutions to three-dimensional generalized MHD equations with large initial data

被引：0
作者：
Fagui Liu
Yu-Zhu Wang
机构：
[1] North China University of Water Resources and Electric Power,School of Mathematics and Statistics
来源：
Zeitschrift für angewandte Mathematik und Physik | 2019年 / 70卷
关键词：
Generalized MHD equations; Global solutions; Stability; 76W05; 76D03;
D O I：
暂无
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学科分类号：
摘要：
We investigate the initial value problem for the three-dimensional generalized incompressible MHD equations. Firstly, global stability result is established by energy method in the Fourier space. Then for a class of large initial data, global solutions are obtained in the critical function space X1-2α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {X}^{1-2\alpha }$$\end{document} by global stability result.
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  • [1] Cai Y(2018)Global well-posedness of the incompressible magnetohydrodynamics Arch. Ration. Mech. Anal. 228 969-993
  • [2] Lei Z(2010)Two regularity criteria for the 3D MHD equations J. Diff. Equ. 248 2263-2274
  • [3] Cao C(2007)The Beale–Kato–Majda criterion to the 3D viscous magneto-hydrodynamics equations Commun. Math. Phys. 275 861-872
  • [4] Wu J(2008)On the regularity criterion of weak solution for the 3D viscous magneto-hydrodynamics equations Commun. Math. Phys. 284 919-930
  • [5] Chen Q(2013)On the global existence for the Muskat problem J. Eur. Math. Soc. 15 201-227
  • [6] Miao C(1972)Inéquations en thermoélasticité et magnétohydrodynamique Arch. Ration. Mech. Anal. 46 241-279
  • [7] Zhang Z(2016)Regularity criteria for the incompressible magnetohydrodynamic equations with partial viscosity Anal. Appl. (Singap.) 14 321-339
  • [8] Chen Q(2005)On the regularity criteria for weak solutions to the magnetohydrodynamic equations J. Diff. Equ. 213 235-254
  • [9] Miao C(2014)On some new global existence results for 3D magnetohydrodynamics equations Nonlinearity 27 343-352
  • [10] Zhang Z(2016)On regularity criteria for the 3D incompressible MHD equations involving one velocity component J. Math. Fluid Mech. 18 187-206
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