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
收藏
页码：1591 / 1611
页数：21
相关论文
共 50 条
[21]   UNIQUE SOLVABILITY OF INITIAL-BOUNDARY VALUE PROBLEM FOR ONE-DIMENSIONAL EQUATIONS OF POLYTROPIC FLOWS OF MULTICOMPONENT VISCOUS COMPRESSIBLE FLUIDS [J].
Mamontov, A. E. ;
Prokudin, D. A. .
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2018, 15 :631-649
[22]   On the global well-posedness for the two-dimensional Boussinesq equations with horizontal dissipation [J].
Guo, Meiqi ;
Zhang, Qian .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (01) :322-345
[23]   GLOBAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF TWO-DIMENSIONAL DENSITY-DEPENDENT BOUSSINESQ EQUATIONS WITH LARGE INITIAL DATA AND VACUUM [J].
Zhong, Xin .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (11) :6713-6745
[24]   Global weak solutions to a two-dimensional compressible MHD equations of viscous non-resistive fluids [J].
Li, Yang ;
Sun, Yongzhong .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (06) :3827-3851
[25]   Global regularity of the two-dimensional regularized MHD equations [J].
Ye, Zhuan .
DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 2019, 16 (02) :185-223
[26]   Eventual Regularity of the Two-Dimensional Boussinesq Equations with Supercritical Dissipation [J].
Jiu, Quansen ;
Wu, Jiahong ;
Yang, Wanrong .
JOURNAL OF NONLINEAR SCIENCE, 2015, 25 (01) :37-58
[27]   Boundary Control Problem for Heat Convection Equations with Slip Boundary Condition [J].
Mallea-Zepeda, Exequiel ;
Lenes, Eber ;
Valero, Elvis .
MATHEMATICAL PROBLEMS IN ENGINEERING, 2018, 2018
[28]   AN INVERSE PROBLEM FOR TWO-DIMENSIONAL EQUATIONS OF FINDING THE THERMAL CONDUCTIVITY OF THE INITIAL DISTRIBUTION [J].
Zaynullov, A. R. .
VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2015, 19 (04) :667-679
[29]   On the Grad-Rubin boundary value problem for the two-dimensional magneto-hydrostatic equations [J].
Alonso-Oran, Diego ;
Velazquez, Juan J. L. .
MATHEMATISCHE ANNALEN, 2024, 388 (03) :2387-2472
[30]   First Boundary Value Problem for the Two-Dimensional Wave Equation [J].
K. B. Sabitov .
Lobachevskii Journal of Mathematics, 2023, 44 :3555-3562
12345