GLOBAL WELL-POSEDNESS FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE MAGNETOHYDRODYNAMIC FLOWS IN BOUNDED DOMAINS

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (6): 1833-1845.

GLOBAL WELL-POSEDNESS FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE MAGNETOHYDRODYNAMIC FLOWS IN BOUNDED DOMAINS

陈德富, 叶霞

College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China

收稿日期:2017-07-17 修回日期:2017-11-13 出版日期:2018-12-25 发布日期:2018-12-28
通讯作者: Xia YE E-mail:yexia@jxnu.edu.cn
作者简介:Defu CHEN,E-mail:chernsing@163.com
基金资助:
Ye was partially supported by NSFC (11701240) and the Natural Science Foundation of Jiangxi Province (2017BAB211001).

GLOBAL WELL-POSEDNESS FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE MAGNETOHYDRODYNAMIC FLOWS IN BOUNDED DOMAINS

Defu CHEN, Xia YE

College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China

Received:2017-07-17 Revised:2017-11-13 Online:2018-12-25 Published:2018-12-28
Contact: Xia YE E-mail:yexia@jxnu.edu.cn
Supported by:
Ye was partially supported by NSFC (11701240) and the Natural Science Foundation of Jiangxi Province (2017BAB211001).

摘要/Abstract

摘要： In this paper, we study the three-dimensional incompressible magnetohydrodynamic equations in a smooth bounded domains, in which the viscosity of the fluid and the magnetic diffusivity are concerned with density. The existence of global strong solutions is established in vacuum cases, provided the assumption that (||▽μ(ρ₀)||_L^p +||▽ν(ρ₀)||_L^q +||b₀||_L³+||ρ₀||_L^∞) (p, q > 3) is small enough, there is not any smallness condition on the velocity.

关键词: incompressible MHD, global solution, small initial data

Abstract: In this paper, we study the three-dimensional incompressible magnetohydrodynamic equations in a smooth bounded domains, in which the viscosity of the fluid and the magnetic diffusivity are concerned with density. The existence of global strong solutions is established in vacuum cases, provided the assumption that (||▽μ(ρ₀)||_L^p +||▽ν(ρ₀)||_L^q +||b₀||_L³+||ρ₀||_L^∞) (p, q > 3) is small enough, there is not any smallness condition on the velocity.

Key words: incompressible MHD, global solution, small initial data

陈德富, 叶霞. GLOBAL WELL-POSEDNESS FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE MAGNETOHYDRODYNAMIC FLOWS IN BOUNDED DOMAINS[J]. 数学物理学报(英文版), 2018, 38(6): 1833-1845.

Defu CHEN, Xia YE. GLOBAL WELL-POSEDNESS FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE MAGNETOHYDRODYNAMIC FLOWS IN BOUNDED DOMAINS[J]. Acta mathematica scientia,Series B, 2018, 38(6): 1833-1845.

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GLOBAL WELL-POSEDNESS FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE MAGNETOHYDRODYNAMIC FLOWS IN BOUNDED DOMAINS

GLOBAL WELL-POSEDNESS FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE MAGNETOHYDRODYNAMIC FLOWS IN BOUNDED DOMAINS

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