• 综合性科技类中文核心期刊
    • 中国科技论文统计源期刊
    • 中国科学引文数据库来源期刊
    • 中国学术期刊文摘数据库(核心版)来源期刊
    • 中国学术期刊综合评价数据库来源期刊
WANG Shu, WANG Na. Boundary Layer Problem of the Incompressible MHD Equations[J]. Journal of Beijing University of Technology, 2017, 43(10): 1596-1603. DOI: 10.11936/bjutxb2016120057
Citation: WANG Shu, WANG Na. Boundary Layer Problem of the Incompressible MHD Equations[J]. Journal of Beijing University of Technology, 2017, 43(10): 1596-1603. DOI: 10.11936/bjutxb2016120057

Boundary Layer Problem of the Incompressible MHD Equations

More Information
  • Received Date: December 26, 2016
  • Available Online: August 03, 2022
  • Published Date: October 09, 2017
  • In this paper, the boundary layer problem of the viscous incompressible MHD equations with non-characteristic boundary condition was studied. In a three-dimensional space the solution to viscous MHD equations approximated by that of the ideal MHD equations in the interior region was studied, and by the solution of the zero order boundary layer equations in the boundary layer as both the viscosity coefficient and magnetic diffusion coefficient ν→0. Moreover, the uniform space and time estimates on the approximation in two-dimensional space was obtained.

  • [1]
    SERMANGE M, TEMAM R. Some mathematical questions related to the MHD equations [J]. Communications on Pure and Applied Mathematics, 1983, 36(5): 635-664. doi: 10.1002/(ISSN)1097-0312
    [2]
    WU J H. Vissous and inviscid magneto-hydrodynamics equations [J]. Journal d'Analyse Mathématique, 1997, 73(1): 251-265. doi: 10.1007/BF02788146
    [3]
    BISKAMP D. Nonlinear magnetohydrodynamics [M]. Cambridge: Cambridge University Press, 1993: 8-95.
    [4]
    HE C, XIN Z P. On the regularity of weak solutions to the magnetohydrodynamic equations[J]. Journal of Differential Equations, 2005, 213(2): 235-254. doi: 10.1016/j.jde.2004.07.002
    [5]
    HE C, XIN Z P. Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations[J]. Journal of Functional Analysis, 2005, 227 (1): 113-152. doi: 10.1016/j.jfa.2005.06.009
    [6]
    WU Z L, WANG S. Zero viscosity and diffusion vanishing limit of the incompressible magnetohydrodynamic system with perfectly conducting wall[J]. Nonlinear Analysis: Real World Applications, 2015, 24: 50-60. doi: 10.1016/j.nonrwa.2015.01.002
    [7]
    GUO B L, WANG G W. Vanishing viscosity limit for the 3D magnetohydrodynamic system with generalized Navier slip boundary condition[J]. Mathematical Methods in the Applied Sciences, 2016, 39 (15): 4526-4534. doi: 10.1002/mma.v39.15
    [8]
    谢晓强, 罗琳, 李常敏.非特征边界的MHD方程的边界层[J].数学年刊, 2014, 35A(2): 171-192. http://www.cnki.com.cn/Article/CJFDTOTAL-SXNZ201402005.htm

    XIE X Q, LUO L, LI C M. Boundary layer for MHD equations with the noncharacteristic boundary[J]. Chinese Annals of Mathematics, 2014, 35A(2): 171-192. (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-SXNZ201402005.htm
    [9]
    TEMAM R, WANG X. Boundary layer associated with the incompressible Navier-Stokes equations: the noncharacteristic boundary case[J]. Journal of Differential Equations, 2002, 179(2): 647-686. doi: 10.1006/jdeq.2001.4038
    [10]
    TEMAM R, WANG X. Remarks on the Prandtl type equations for a permeable wall[J]. Zeitschrift fur Angewandte Mathematik und Mechanik, 2000, 80(11/12): 835-843.
    [11]
    谢晓强, 张蕾.不可压流体的边界层问题[J].数学年刊, 2009, 30A(3): 309-332. http://www.cnki.com.cn/Article/CJFDTOTAL-SXNZ200903005.htm

    XIE X Q, ZHANG L. Boundary layer associated with incompressible flows[J]. Chinese Annals of Mathematics, 2009, 30A(3): 309-332. (in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-SXNZ200903005.htm
    [12]
    TEMAM R, WANG X M. Asymptotic analysis of Oseen type equations in a channel at small viscosity[J]. Indiana University Mathematics Journal, 1996, 45(45): 863-916.
  • Cited by

    Periodical cited type(2)

    1. 王娜,王术. 平面平行管道中的MHD方程组的边界层. 数学物理学报. 2019(04): 738-760 .
    2. 沈林,王术. 一类三种群捕食系统正解的存在性. 北京工业大学学报. 2019(10): 1025-1032 . 本站查看

    Other cited types(0)

Catalog

    Article views (225) PDF downloads (74) Cited by(2)

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return