[1] Alfvén H. Existence of electromagnetic-hydrodynamic waves. Nature, 1942, 150:405-406
[2] Amosov A A, Zlotnik A A. A difference scheme on a non-uniform mesh for the equations of one-dimensional magnetic gas dynamics. USSR Compu Maths Math Phys, 1990, 29(2):129-139
[3] Antontsev S N, Kazhikhov A V, Monakhov V N. Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, Studies in Mathematics and Its Applications. Vol. 22. Amsterdam:North-Holland Publishing Co, ISBN 0-444-88382-7, 1990; translated from the Russian
[4] Bittencourt J A. Fundamentals of Plasma Physics. 3rd. New York:Spinger-Verlag, 2004
[5] Boyd T J M, Sanderson J J. The Physics of Plasmas. Cambridge:Cambridge Univ Press, 2003
[6] Cabannes H. Theoretical Magnetofluiddynamics. New York:Academic Press, 1970
[7] Cercignani C, Illner R, Pulvirenti M. The Mathematical Theory of Dilute Gases//Appl Math Sci 106. New York:Springer-Verlag, 1994
[8] Chandrasekhar S. Hydrodynamic and Hydromagnetic Stability. Oxford:Oxford Univ Press, 1961
[9] Chen G Q, Wang D. Global solution of nonlinear magnetohydrodynamics with large initial data. J Differential Equations, 2002, 182:344-376
[10] Chen G Q, Wang D. Existence and continuous dependence of large solutions for the magnetohydrodynamic equations. Z Angew Math Phys, 2003, 54:608-632
[11] Chapman S, Colwing T G. The Mathematical Theory of Nonuniform Gases. 3rd ed. Cambridge, UK:Cambridge Math Lib, Cambridge University Press, 1990
[12] Ducomet B, Feireisl E. The equations of magnetohydrodynamics:On the interaction between matter and radiation in the evolution of gaseous stars. Commun Math Phys, 2006, 266:595-629
[13] Fan J, Jiang S, Nakamura G. Vanishing shear viscosity limit in the magnetohydrodynamic equations. Commun Math Phys, 2007, 270:691-708
[14] Fan J, Yu W. Global variational solutions to the compressible magnetohydrodynamic equations. Nonlinear Anal, 2008, 69:3637-3660
[15] Fan J, Yu W. Strong solution to the compressible MHD equations with vacuum. Nonlinear Anal Real World Appl, 2009, 10:392-409
[16] Freidberg J P. Ideal Magneto-hydrodynamic Theory of Magnetic Fusion Systems//Rev Modern Physics Vol. 54, No 3. The American Physical Society, 1982
[17] Grad H. Asymptotic Theory of the Boltzmann Equation Ⅱ//Laurmann J A. Rarefied Gas Dynamics. 2ed. New York:Academic Press, 1963
[18] Gunderson R M. Linearized Analysis of One-Dimensional Magnetohydrodynamic Flows. Springer Tracts in Natural Philosophy. Vol. 1. Berlin. Gottingen. Heidelberg. New York:Springer-Verlag, 1964
[19] Hu X, Wang D. Global solutions to the three-dimensional full compressible magnetohydrodynamic flows. Commun Math Phys, 2008, 283:255-284
[20] Hu X, Wang D. Compactness of weak solutions to the three-dimensional compressible magnetohydrodynamic equations. J Differential Equations, 2008, 245:2176-2198
[21] Hu X, Wang D. Low mach number limit of viscous compressible magnetohydrodynamic flows. SIAM J Math Anal, 2009, 41:1272-1294
[22] 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
[23] Huang F M, Zhao H J. On the global stability of contact discontinuity for compressible Navier-Stokes equations. Rend Sem Mat Univ Padova, 2003, 109:283-305
[24] Iskenderova D A. An initial-boundary value problem for magnetogasdynamic equations with degenerate density. Differetial Eqns, 2000, 36:847-856
[25] Jiang S, Ju Q C, Li F C. Incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. Commun Math Phys, 2010, 297:371-400
[26] Kawashima S. Smooth global solutions for two-dimensional equations of electromagneto-fluid dynamics. Japan J Appl Math, 1984, 1:207-222
[27] Kawashima S, Okada M. Smooth global solutions for the one-dimensional equations in magnetohydrodynamics. Proc Japan Acad Ser A Math Sci, 1982, 58:384-387
[28] Kawashima S, Shizuta Y. Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid. Tsukuba J Math, 1986, 10:131-149
[29] Kawashima S, Shizuta Y. Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid Ⅱ. Proc Japan Acad Ser A, 1986, 62:181-184
[30] Kazhikhov A V. A priori estimates for the solutions of equations of magneticgasdynamics, boundary value problems for equations of mathematical physics. Krasnoyarsk, 1987. In Russian
[31] Kazhikhov A V, Smagulov S S. Well-posedness and approximation methods for a model of magnetogasdy-namics. Izv Akad Nauk Kazakh SSR Ser Fiz -Mat, 19865:17-19
[32] Landau L D, Lifshitz E M, Pitaevskii L P. Electrodynamics of Continuous Media. 2nd ed. London:Butterworth-Heinemann, 1999
[33] Li H L, Xu X Y, Zhang J W. Global classsical solutions to 3D compressible magnetohydrodynamic equations with large oscillations and vacuum. SIAM J Math Anal, 2013, 45:1356-1387
[34] Lin F, Zhang P. Global small solutions to an MHD-type system:the three-dimensional case. Comm Pure Appl Math, 2014, 67:531-580
[35] Lin F, Zhang T. Global small solutions to a complex fluid model in three dimensional. Arch Ration Mech Anal, 2015, 216:905-920
[36] Liu H, Yang T, Zhao H, Zou Q. One-dimensional compressible Navier-Stokes equations with temperature dependent transport coefficients and large data. SIAM J Math Anal, 2014, 46:2185-2228
[37] Matsumura A, Nishida T. The initial value problem for the equations of motion of viscous and heatconductive gases. J Math Kyoto Univ, 1980, 20:67-104
[38] Nishihara K, Yang T, Zhao H J. Nonlinear stability of strong rarefaction waves for compressible NavierStokes equations. SIAM J Math Anal, 2004, 35:1561-1597
[39] Umeda T, Kawashima S, Shizuta Y. On the decay of solutions to the linearized equations of electromagnetofluid dynamics. Japan J Appl Math, 1984, 1:435-457
[40] Vincenti W G, Kruger J C H. Introduction to Physical Gas Dynamics. New York:John Wiley and Sons, 1965
[41] Vol'pert A I, Khudiaev S I. On the Cauchy problem for composite systems of nonlinear equations. Mat Sb, 1972, 87:504-528
[42] Wang D. Large solutions to the initial-boundary value problem for planar magnetohydrodynamics. SIAM J Appl Math, 200, 63:1424-1441
[43] Xu L, Zhang P. Global small solutions to three-dimensional incompressible magnetohydrodynamical system. SIAM J Math Anal, 2015, 47:26-65
[44] Zhang J W, Jiang S, Xie F. Global weak solutions of an initial boundary value problem for screw pinches in plasma physics. Math Models Methods Appl Sci, 2009, 19:833-875
[45] Zhang J W, Zhao J N. Some decay estimates of solutions for the 3-D compressible isentropic magnetohydrodynamics. Commun Math Sci, 2010, 8:835-850
[46] Zhang J W, Zhao X K. On the global solvability and the non-resistive limit of the one-dimensional compressible heat-conductive MHD equations. J Math Phys, 2017, 58:031504 |