INITIAL BOUNDARY VALUE PROBLEM FOR TWO-DIMENSIONAL VISCOUS BOUSSINESQ EQUATIONS FOR MHD CONVECTION

被引：29

作者：

Bian, Dongfen ^{[1
,2
]}

机构：

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2016年 / 9卷 / 06期

基金：

中国国家自然科学基金;

关键词：

MHD Boussinesq system; weak solution; global regularity; uniqueness; GLOBAL WELL-POSEDNESS; MAGNETOHYDRODYNAMIC EQUATIONS; THERMAL-DIFFUSIVITY; MAGNETIC DIFFUSION; PARTIAL VISCOSITY; SYSTEM; REGULARITY; EXISTENCE;

D O I：

10.3934/dcdss.2016065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the initial boundary value problem for two-dimensional viscous Boussinesq equations for MHD convection. We show that the system has a unique classical solution for H-3 initial data, and the non-slip boundary condition for velocity field and the perfectly conducting wall condition for magnetic field. In addition, we show that the kinetic energy is uniformly bounded in time.

引用

页码：1591 / 1611

页数：21

共 33 条

[1] On the global well-posedness for Boussinesq system [J].

Abidi, H. ;

Hmidi, T. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 233 (01) :199-220

[2]

Adams R.A., 1975, Sobolev Spaces

[3]

[Anonymous], 1968, LINEAR QUASILINEAR E

[4]

Bian D., 2015, PREPRINT

[5] On 2-D Boussinesq equations for MHD convection with stratification effects [J].

Bian, Dongfen ;

Gui, Guilong .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (03) :1669-1711

[6] GLOBAL EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTIONS TO THE ELECTRIC-MAGNETOHYDRODYNAMIC EQUATIONS [J].

Bian, Dongfen ;

Guo, Boling .

[7]

Cannon J., 1980, Lecture Notes in Math., V771, P129

[8] Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion [J].

Cao, Chongsheng ;

Wu, Jiahong .

ADVANCES IN MATHEMATICS, 2011, 226 (02) :1803-1822

[9] Global regularity for the 2D Boussinesq equations with partial viscosity terms [J].

Chae, Dongho .

ADVANCES IN MATHEMATICS, 2006, 203 (02) :497-513

[10] The Beale-Kato-Majda criterion for the 3D magneto-hydrodynamics equations [J].

Chen, Qionglei ;

Miao, Changxing ;

Zhang, Zhifei .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 275 (03) :861-872

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