[1] Liu J G, Pego R. Stable discretization of magnetohydrodynamics in bounded domains. Comm Math Sci, 2010, 8: 234-251
[2] Wang S, Xu Z L. Low Mach numberlimit of non-isentropic magnetohydrodynamic equations in a bounded domain. Nonlinear Analysis, 2004, 105: 102-119
[3] Fan J, Gao H J, Guo B L. Low Mach number limit of the compressible magnetohydrodynamic equations with zero thermal conductivity coefficient. Mathematical Methods in the Applied Sciences. 2011, 11: 2181- 2188
[4] Jiang S, Ju Q C, Li F C. Low Mach number limit for the multi-dimensional full magnetohydrodynamic equations. Nonlinearity, 2012, 25: 1351-1365
[5] Jiang S, Ju Q C, Li F C, et al. Low Mach number limit for the multi-dimensional full magnetohydrodynamic equations with general initial data. Adv Math, 2014, 259: 384-420
[6] Dou C S, Ju Q C. Low Mach number limit for the compressible magnetohydrodynamic equation in a bounded domain for all time. Commun Math Sci, 2014, 12: 661-679
[7] Chen G Q, Wang D H. Global solutions of nonlinear magnetohydrodynamics with large initial data. J Diff Eq, 2002, 182: 344-376
[8] 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
[9] Fan J, Jiang S, Nakamura G. Vanishing shear viscosity limit in the magnetohydrodynamic equations. Comm Math Phys, 2007, 270: 691-708
[10] Hoff D, Tsyganov E. Uniqueness and continuous dependence of weak solutions in compressible magneto- hydrodynamics. Z Angew Math Phys, 2005, 56: 791-804
[11] Hu W R. Cosmic magnetohydrodynamics. Beijing: Science Press, 1987 (in Chinese)
[12] Kawashima S. Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics [Ph D Thesis]. Kyota University, 1983
[13] Laudau L D, Lifshitz E M. Electrodynamics of Continuous Media. 2nd ed. New York: Pergamon, 1984
[14] Zhang J W, Jiang S, Xie F. Global weak solutions of an initial boundary value problem for screw pinches in plasma physics. Math Models Meth Appl Sci, 2009, 19: 833-875
[15] Hu X P,Wang D H. 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
[16] Suen A, Hoff D. Global low-energy weak solutions of the equations of three-dimensional compressible magnetohyfrodynamics. Arch Ration Mech Anal, 2012
[17] Hu X P, Wang D H. Low Mach number limit of viscous compressible magnetohydrodynamic flows. SIAM J Math Anal, 2009, 41: 1272-1294
[18] 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
[19] Matsumura A, Nishida T. Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids. Comm Math Phys, 1983, 89: 445-464
[20] Zajaczkowski W M. On nonstationary motion of a compressible baratropic viscous fluids with boundary slip condition. J Appl Anal, 1998, 4: 167-204
[21] Feireisl E, Novotný A, Petzeltová H. On the existence of globally defined weak solutions to the Navier-Stokes equations. J Math Fluid Mech, 2001, 3: 358-392
[22] Jiang S, Zhang P. Global spherically symmetry solutions of the compressible isentropic Navier-Stokes equations. Comm Math Phys, 2001, 215: 559-581
[23] 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
[24] Lions P -L. Mathematical topics in fluid mechanics. Vol 1: incompressible models, Oxford Lecture Series in Mathematics and its Applications 3. New York: The Clarendon Press and Oxford University Press, 1996
[25] Alazard T. Low Mach number limit of the full Navier-Stokes equations. Arch Ration Mech Anal, 2006, 180: 1-73
[26] Bresch D, Desjardins B, et al. Low Mach number limit of viscous polytropic flows: formal asymptotics in the periodic case. Stud Appl Math, 2002, 109: 125-149
[27] Danchin R. Low Mach number limit for viscous compressible flows. Math Model Numer Anal, 2005, 39: 459-475
[28] Desjardins B, Grenier E. Low Mach number limit of viscous compressible flows in the whole space. R Soc Lond Proc Ser A Math Phys Eng Sci, 1999, 455: 2271-2279
[29] Desjardins B, Grenier E, et al. Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions. J Math Pures Appl, 1999, 78: 461-471
[30] Feireisl E, Novotný A. Singular Limits in Thermodynamics of Viscous Fluids. Basel: Birkhauser, 2009
[31] Hagstrom T, Lorenz J. On the stability of approximate solutions of hyperbolic-parabolic systems and the all-time existence of smooth, slightly compressible flows. Indiana Univ Math J, 2002, 51: 1339-1387
[32] Jiang S, Ou Y B. Incompressible limit of the non-isentropic Navier-Stokes equations with well-prepared initial data in three-dimensional bounded domains. J Math Pures Appl, 2011, 96: 1-28
[33] Kim H, Lee J. The incompressible limits of viscous polytropic fluids with zero thermal conductivity coeffient. Comm PDE, 2005, 30: 1169-1189
[34] Klainerman S, Majda A. Singular perturbations of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm Pure ApplMath, 1981, 34: 481-524
[35] Lions P -L, Masmoudi N. Incompressible limit for a viscous compressible fluid. J Math Pures Appl, 1998, 77: 585-627
[36] Masmoudi N. Examples of singular limits in hydrodynamics//Handbook of Differential Equations: Evolu- tionary equations. Vol III. Amsterdam: Elsevier/North-Holland, 2007: 195-275
[37] Ou Y B. Low Mach number limit of viscous polytropic fluid flows. J Diff Eq, 2011, 251: 2037-2065
[38] Ou Y B. Incompressible limits of the Navier-Stokes equations for all time. J Diff Eq, 2009, 247: 3295-3314
[39] Galdi G P. An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol I. Linearized Steady Problems, New York: Springer-Verlag, 1994
[40] Valli A. Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method. Ann Scuola Norm Sup Pisa CI Sci, 1983, 10(4): 607-647
[41] Valli A, Zajaczkowski W M. Navier-Stokes equations for the compressible fluids: global existence and qualitative properties of the solutions in the general case. Comm Math Phys, 1986, 103: 259-296 |