数学季刊 ›› 2023, Vol. 38 ›› Issue (3): 290-310.doi: 10.13371/j.cnki.chin.q.j.m.2023.03.004

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具有非线性边界条件的不可压 MHD-Boussinesq方程组初边值问题的整体适定性#br#

  

  1. Department of Mathematics, Faculty of Science, Beijing University of Technology,
    Beijing 100124, China
  • 收稿日期:2023-08-04 出版日期:2023-09-30 发布日期:2023-09-30
  • 通讯作者: WANG Shu (1968-), male, native of Nanyang, Henan, professor of Beijing University of Technology, Ph.D supervisor, Ph.D, engages in PDE. E-mail: wangshu@bjut.edu.cn
  • 作者简介: WANG Shu (1968-), male, native of Nanyang, Henan, professor of Beijing University of Technology, Ph.D supervisor, Ph.D, engages in PDE. SUN Rui (2000-), male, native of Zaozhuang, Shandong, graduate student of Beijing University of Technology, under postgraduate, engages in PDE.
  • 基金资助:
    Supported by National Natural Science Foundation of China (Grant Nos. 11831003, 12171111); Natural Science Foundation of Beijing in China (Grant No. KZ202110005011).

Global Well-Posedness of the Initial-Boundary Value Problem on Incompressible MHD-Boussinesq Equations with Nonlinear Boundary Conditions

  1. Department of Mathematics, Faculty of Science, Beijing University of Technology,
    Beijing 100124, China
  • Received:2023-08-04 Online:2023-09-30 Published:2023-09-30
  • Contact: WANG Shu (1968-), male, native of Nanyang, Henan, professor of Beijing University of Technology, Ph.D supervisor, Ph.D, engages in PDE. E-mail: wangshu@bjut.edu.cn
  • About author:WANG Shu (1968-), male, native of Nanyang, Henan, professor of Beijing University of Technology, Ph.D supervisor, Ph.D, engages in PDE. SUN Rui (2000-), male, native of Zaozhuang, Shandong, graduate student of Beijing University of Technology, under postgraduate, engages in PDE.
  • Supported by:
    Supported by National Natural Science Foundation of China (Grant Nos. 11831003, 12171111); Natural Science Foundation of Beijing in China (Grant No. KZ202110005011).

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摘要： The global well-posedness of another class of initial-boundary value problem on two/three-dimensional incompressible MHD-Boussinesq equations in the bounded domain with the smooth boundary is studied. The existence of a class of global weak solution to the initial boundary value problem for two/three-dimensional incompressible MHD-Boussinesq equation with the given pressure-velocity’s relation boundary condition for the fluid field, one generalized perfectly conducting boundary condition for the magnetic field and one density/temperature-velocity’s relation boundary condition for the density/temapture at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case for the smooth initial data is also proven.

关键词:  Global weak solution, Global smooth solution, Incompressible MHD-Boussinesq equations

Abstract: The global well-posedness of another class of initial-boundary value problem on two/three-dimensional incompressible MHD-Boussinesq equations in the bounded domain with the smooth boundary is studied. The existence of a class of global weak solution to the initial boundary value problem for two/three-dimensional incompressible MHD-Boussinesq equation with the given pressure-velocity’s relation boundary condition for the fluid field, one generalized perfectly conducting boundary condition for the magnetic field and one density/temperature-velocity’s relation boundary condition for the density/temapture at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case for the smooth initial data is also proven.

Key words:  Global weak solution, Global smooth solution, Incompressible MHD-Boussinesq equations

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