二维等温可压缩磁流体方程组的不可压极限

详细信息    查看全文 | 推荐本文 |

英文篇名：Incompressible Limit of 2-d Isothermal Magnetohydrodynamic Equations 作者：王昕 ; 胡玉玺 英文作者：WANG XIN;HU YUXI;College of Science, Beijing Information Science and Technology University;College of Science, China University of Mining and Technology; 关键词：等温磁流体 ; 不可压极限 ; 好始值 ; 理想导体边界条件 英文关键词：Isothermal magnetohydrodynamic equations;;incompressible limit;;well-prepared data;;perfectly conducted boundary condition 中文刊名：YYSU 英文刊名：Acta Mathematicae Applicatae Sinica 机构：北京信息科技大学理学院;中国矿业大学(北京)理学院; 出版日期：2019-01-15 出版单位：应用数学学报 年：2019 期：v.42 基金：国家自然科学基金(71501016,11701556);; 北京信息科技大学“勤信人才”培育计划(QXTCP B201705)资助项目 语种：中文; 页：YYSU201901007 页数：15 CN：01 ISSN：11-2040/O1 分类号：87-101

摘要

我们考虑二维等温可压缩磁流体方程组的不可压极限问题.在好始值以及理想导体边界条件下,我们证明了当马赫数趋于零时,可压缩磁流体方程组的弱解收敛到不可压缩磁流体方程组的强解并且得到了相应的收敛率.
        We consider the incompressible limit of 2-d isothermal magnetohydrodynamic equations. If the initial data is well-prepared, we show that the weak solutions of the compressible magnetohydrodynamic equations under the perfectly conducted boundary condition converge to the strong solutions of incompressible system as Mach number goes to zero.The convergence rates are also obtained.

引文

[1] Ducomet, B, Feireisl, E. The equations of magnetohydrodynamics:On the interaction between matter and radiation in the evolution of gaseous stars. Comm. Math. Phys.,2006, 266:595-629
    [2] Fan J, Jiang, S,Nakamura G. Vanishing shear viscosity limit in the magnetohydrodynamic equations.Commun. Math. Phys.,2007, 270:691-708
    [3] Hu, X, Wang, D. Global solutions to the three-dimensional full compressible magnetohydrodynamic flows. Comm. Math. Phys.,2008, 283:255-284
    [4] Hu, X, Wang, D. Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic flows. Arch. Ration. Mech. Anal., 2010, 197:203-238
    [5] Li, H, Xu, X, Zhang, J. Global classical solutions to 3D compressible magnetohydrodynamic equations with large oscillations and vacuum. SIAM J. Math. Anal., 2013, 45:1356-1387
    [6] Hu, X, Wang, D. Low Mach number limit of viscous compressible magnetohydrodynamic flows. SIAM J. Math. Anal., 2009, 41:1272-1294
    [7] Jiang, S, Ju, Q C, Li, F C. Incompressible Limit of the Compressible Magnetohydrodynamic Equations with Periodic Boundary Conditions. Comm. Math. Phys., 2010, 297:371-400
    [8] Jiang S, Ju Q C, Li F C. Incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients. SIAM J. Math. Anal.,2010, 42:2539-2553
    [9] Feireisl E, Novotny, A, Petzeltova, H. On the existence of globally defined weak solutions to the Navier-Stokes equations. J. Math. Fluid Mech.,2001, 3:358-392
    [10] Jiang S, Zhang P. Remarks on weak solutions to the Navier-Stokes equations for 2-D compressible isothermal fluids with spherically symmetric initial data. Indiana Univ. Math. J.,2002, 51:345-355
    [11] Jiang, S, Zhang, P. On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations. Comm. Math. Phys., 2001, 215:559-581
    [12] Jiang, S, Zhang, P. Axisymmetric solutions of the 3-D Navier-Stokes equations for compressible isentropic fluids. J. Math. Pures Appl., 2003, 82:949-973
    [13] Lions P L. Mathematical topics in fluid mechanics. Vol. 1. Incompressible models. New York:Oxford University Press, 1996
    [14] Lions P L. Mathematical topics in fluid mechanics. Vol.2. Compressible models. New York:Oxford University Press, 1998
    [15] Ebin D G. Motion of a slightly compressible fluid. Proc. atl. Acad. Sci.,1975, 72(2):539-542
    [16] Klainerman, S, Majda, A. Singular perturbations of quasilinear hyperbolic systems with large parameters and the incom-pressible limit of compressible fluids. Comm. Pure Appl. Math., 1981, 34:481-524
    [17] Klainerman, S, Majda, A. Compressible and incompressible fluids. Comm. Pure Appl. Math.,1982,35:629-653
    [18] Plotnikov P I, Weigant W. Isothermal Navier-Stokes Euqations and Radon Transform, SIAM J.Math. Anal.,2015, 47:626-653