Xin XU
. CONVERGENCE FROM AN ELECTROMAGNETIC FLUID SYSTEM TO THE FULL COMPRESSIBLE MHD EQUATIONS[J]. Acta mathematica scientia, Series B, 2018
, 38(3)
: 805
-818
.
DOI: 10.1016/S0252-9602(18)30785-9
[1] Cabannes H. Theoretical Magnetohydrodynamics. New York:Academic Press, 1970
[2] Imai I. General principles of magneto-fluid dynamics//Magneto-Fulid Dynamics. Suppl Prog Theor Phys, 1962, 1-34
[3] Jang J, Masmoudi N. Derivation of Ohm's law from the kinetic equations. SIAM J Math Anal, 2012, 44(5):3649-3669
[4] Kawashima S. System of a Hyperbolic-Parabolic Composite Type, with Applications to the Equations of Manetohydrodynamics[D]. Kyoto:Kyoto University, 1983
[5] Li F C, Yu H J. Optimal decay rate of classical solutions to the compressible magnetohydrodynamic equations. Proc R Soc Edinb, 2011, 141A:109-126
[6] 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
[7] Hu X P, Wang D H. Global solutions to the three-dimensional full compressible magnetohydrodynamic flows. Commun Math Phys, 2008, 283:255-284
[8] 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
[9] Fan J, Yu W. Strong solution to the compressible MHD equations with vacuum. Nonlinear Anal Real World Appl, 2009, 10:392-409
[10] Hu X P, Wang D H. Low mach number limit of viscous compressible magnetohydrodynamic flows. SIAM J Math Anal, 2009, 41:127-1294
[11] 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
[12] Xiao Y L, Xin Z P, Wu J H. Vanishing viscosity limit for the 3D magnetohydrodynamic system with a slip boundary condition. J Funct Anal, 2009, 257(11):3375-3394
[13] Cannone M, Chen Q L, Miao C X. A losing estimate for the ideal MHD equations with application to blow-up criterion[J/OL]. SIAM J Math Anal, 2007, 38(6):1847-1859
[14] Lei Z, Zhou Y. BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity. Discrete Contin Dyn Syst, 2009, 25(2):575-583
[15] Kawashima S, Shizuta Y. Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid. Tsukuba J Math, 1986, 10(1):131-149
[16] Kawashima S, Shizuta Y. Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid Ⅱ. Proc Jpn Acad Ser A, 1986, 62:181-184
[17] Jiang S, Li F C. Rigorous derivation of the compressible magnetohydrodynamic equations from the electromagnetic fluid system. Nonlinearity, 2012, 25:1735-1752
[18] Jiang S, Li F C. Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations. Asymptotic Analysis, 2015, 95:161-185
[19] Jiang S, Li F C. Zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system. Sci China Math, 2015, 58(1):61-76
[20] Masmoudi M. Global well posedness for the Maxwell-Navier-Stokes system in 2D. J Math Pures Appl, 2010, 93:559-571
[21] Xu X. On the large time behavior of the electromagnetic fluid system in R3. Nonlinear Analysis:Real World Applications, 2017, 33:83-99