磁气体动力学欧拉方程组Riemann解磁场消失的极限
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摘要
证明了理想非等熵磁气体动力学守恒律方程组当磁场作用消失时,其Riemann问题的解收敛于相应的绝热流可压缩欧拉方程组的解,即气体动力学欧拉方程组Riemann解关于磁场强度的稳定性.
This paper is concerned with the ideal non-isentropic magnetogasdynamics as magnetic field vanishes. We prove the solutions of the Riemann problem converge to the corresponding Riemann solutions of adiabatic compressible Euler equations, which indicates the stability on the magnetic field intensity of the Euler equations in gas dynamics.
This paper is concerned with the ideal non-isentropic magnetogasdynamics as magnetic field vanishes. We prove the solutions of the Riemann problem converge to the corresponding Riemann solutions of adiabatic compressible Euler equations, which indicates the stability on the magnetic field intensity of the Euler equations in gas dynamics.
引文
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[2] Cowling T G. Magnetodrodynamics[M]. New York:Interscience, 1957.
[3]胡文瑞.宇宙磁流体力学[M].北京:科学出版社,1987.
[4]李大潜,秦钱虎,物理学与偏微分方程[M].北京:高等教育出版社,2003.
[5]吴其芬,李桦.磁流体力学[M].长沙:国防科技大学出版社,2007.
[6]胡燕波,盛万成.磁气体动力学守恒律方程组的基本波[J].应用数学与计算数学学报,2009,23(2):49-54.
[7] Hu Y B, Sheng W C. The Riemann problem of conservation laws in magetogasdynamics[J].Commun Pure Appl Anal, 2013, 12:755-769.
[8] Chang T, Hsiao L. Riemann problem for one dimensional adiabatic flow without convexity[J].Acta Math Sinica, 1979, 22:712-732.
[9] Kennel C F, Blandford R D, Coppi P. MHD intermediate shock discontinuities. Part 1:Rankine-Hugoniot conditions[J]. Plasma Phys, 1989, 42:299-319.
[10] Shen Chun. The limits of Riemann solutions to the isentropic magnetogasdynamics[J]. Applied Mathematics Letters, 2011, 24:1124-1129.
[11] Chang T, Hsiao T. The Riemann problem and interaction of waves in gas dynamics[M]//Pitman Monographs and Surveys in Pure and Applied Mathematics. 41. New York:Harlow Longman Scientific and Technical, 1989.
[12]贝特曼.磁流体力学不稳定性[M].徐复,等译.北京:原子能出版社,1982.
[2] Cowling T G. Magnetodrodynamics[M]. New York:Interscience, 1957.
[3]胡文瑞.宇宙磁流体力学[M].北京:科学出版社,1987.
[4]李大潜,秦钱虎,物理学与偏微分方程[M].北京:高等教育出版社,2003.
[5]吴其芬,李桦.磁流体力学[M].长沙:国防科技大学出版社,2007.
[6]胡燕波,盛万成.磁气体动力学守恒律方程组的基本波[J].应用数学与计算数学学报,2009,23(2):49-54.
[7] Hu Y B, Sheng W C. The Riemann problem of conservation laws in magetogasdynamics[J].Commun Pure Appl Anal, 2013, 12:755-769.
[8] Chang T, Hsiao L. Riemann problem for one dimensional adiabatic flow without convexity[J].Acta Math Sinica, 1979, 22:712-732.
[9] Kennel C F, Blandford R D, Coppi P. MHD intermediate shock discontinuities. Part 1:Rankine-Hugoniot conditions[J]. Plasma Phys, 1989, 42:299-319.
[10] Shen Chun. The limits of Riemann solutions to the isentropic magnetogasdynamics[J]. Applied Mathematics Letters, 2011, 24:1124-1129.
[11] Chang T, Hsiao T. The Riemann problem and interaction of waves in gas dynamics[M]//Pitman Monographs and Surveys in Pure and Applied Mathematics. 41. New York:Harlow Longman Scientific and Technical, 1989.
[12]贝特曼.磁流体力学不稳定性[M].徐复,等译.北京:原子能出版社,1982.