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#

doi:10.13371/j.cnki.chin.q.j.m.2023.03.004

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

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#

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

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).

摘要/Abstract

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

中图分类号:

O175.2

王术, 孙瑞. 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#[J]. 数学季刊, 2023, 38(3): 290-310.

WANG Shu, SUN Rui. Global Well-Posedness of the Initial-Boundary Value Problem on Incompressible MHD-Boussinesq Equations with Nonlinear Boundary Conditions[J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 290-310.

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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#

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

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